A data-driven sponge fiber temperature control parameter optimization method

Abstract

This invention relates to the field of general control or regulation system technology, specifically to a data-driven method for optimizing temperature control parameters of sponge fibers. By constructing a spatial topology map using multi-node temperature sensors within the heating furnace, the real-time acquired multidimensional temperature sequence is input into a spatiotemporal graph neural network to extract spatial adjacency heat conduction characteristics and temporal lag characteristics, outputting a predicted temperature field distribution matrix for a future set step size. The deviation between this matrix and the target curing temperature curve is calculated to generate an error matrix. Based on the error matrix, an inverse dynamics model is used to solve for and output the power adjustment increment of the actuators in each heating zone. This, combined with real-time temperature feedback, forms a feedforward-feedback composite control closed loop. This method enables the pre-prediction of the future temperature distribution in unmeasured areas within the sponge fiber, allowing the control system to adjust the power of each heating zone in advance based on future deviations. This overcomes the control lag caused by the material's low thermal conductivity and avoids local temperature overshoot and uneven curing.

Description

Technical Field

[0001] This invention relates to the field of general control or regulation system technology, and specifically to a data-driven method for optimizing temperature control parameters of sponge fibers. Background Technology

[0002] The curing process of sponge fibers in a heating furnace requires a strictly controlled temperature environment. Current industrial temperature control typically uses single-point or a few temperature measurement points to collect data and performs feedback regulation based on a proportional-integral-derivative (PID) algorithm. A limited number of thermocouples are arranged within the furnace to collect temperature values ​​at specific locations. These values ​​are then compared to a preset temperature curve, and the resulting deviation is used to calculate the output control quantity, adjusting the actuator power or valve opening of the corresponding heating zone. When the thickness of the sponge fibers increases or the fabric feeding speed changes, operators usually adjust the PID parameters or reduce the overall heating rate based on experience to avoid surface overheating. This control logic relies entirely on temperature feedback from specific locations; the control system only responds to temperature deviations that have already occurred.

[0003] Sponge fibers are porous materials with low thermal conductivity, resulting in significant time lag and spatial gradients in internal heat transfer during heating. Existing single-point temperature feedback control methods cannot detect the actual temperature state in areas within the fiber where no temperature measuring points are located. When the surface temperature is detected as meeting the standard, the internal temperature often fails to meet curing requirements. Furthermore, when the surface temperature deviates due to continuous heating, a large amount of heat may have accumulated internally, leading to a violent exothermic cross-linking reaction in subsequent stages, causing localized temperature runaway. Current control systems lack a mechanism to predict the spatial distribution and time lag characteristics of heat conduction within the material, making it difficult to intervene in the power distribution of each heating zone before localized overheating occurs, potentially leading to localized scorching or uneven overall curing of thick-section sponge fibers. Summary of the Invention

[0004] The purpose of this invention is to provide a data-driven method for optimizing temperature control parameters of sponge fibers, which can effectively solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A data-driven method for optimizing temperature control parameters of sponge fibers, comprising: A spatial topology map is constructed by deploying multi-node temperature sensors inside the heating furnace. The real-time acquired multidimensional temperature sequence is input into the spatiotemporal graph neural network to extract the spatial adjacency heat conduction characteristics and temporal lag characteristics between nodes; The trained spatiotemporal neural network model is used to output the predicted temperature field distribution matrix for a future set step size; The deviation between the predicted temperature field distribution matrix and the target curing temperature curve is calculated to generate an error matrix; Based on the error matrix, the power adjustment increment of each heating zone actuator is obtained by inversely solving the problem using the inverse dynamics model. The power adjustment increment is added to the current power base and sent to the actuators of each heating zone, forming a feedforward-feedback composite control closed loop in combination with real-time temperature feedback.

[0006] Preferably, the step of constructing a spatial topology map by arranging multi-node temperature sensors within the heating furnace includes: Obtain the physical installation coordinates of the multi-node temperature sensor within the heating furnace; Calculate the Euclidean distance between each pair of nodes based on the physical installation coordinates and generate an initial distance matrix; Set a preset distance threshold, mark the nodes in the initial distance matrix whose Euclidean distance is less than the preset distance threshold as adjacent nodes, and generate an initial adjacency matrix; An adaptive degree centrality algorithm is introduced to calculate the local connection weights of each node, and the edge weights in the initial adjacency matrix are updated using the local connection weights to generate the spatial topology graph.

[0007] Preferably, the step of inputting the real-time acquired multidimensional temperature sequence into a spatiotemporal graph neural network to extract spatial adjacency heat conduction features and temporal lag features between nodes includes: The spatiotemporal graph neural network includes a graph convolutional layer, a gated recurrent unit layer, and a multi-head attention mechanism layer connected in sequence. The multidimensional temperature sequence is input into the graph convolutional layer, and the node features are aggregated based on the edge weights in the spatial topology graph to output the spatial adjacency heat conduction features. The spatial adjacency heat conduction feature is input into the gated loop unit layer, and the retention and forgetting of historical time sequence information are controlled by the update gate and the reset gate, and the time sequence lag feature is output. The temporal lag features are input into the multi-head attention mechanism layer, and global attention weights are assigned to the temporal lag features of different nodes, outputting a spatiotemporal fusion feature vector.

[0008] Preferably, the step of outputting a predicted temperature field distribution matrix with a predetermined future step size using the trained spatiotemporal graph neural network model includes: Obtain the current power input sequence of the actuators in each heating zone of the heating furnace; The current power input sequence and the spatiotemporal fusion feature vector are concatenated along the feature dimension to generate a joint feature matrix; The joint feature matrix is ​​input into the fully connected layer at the end of the spatiotemporal graph neural network model; The joint feature matrix is ​​nonlinearly mapped by the fully connected layer, and the predicted temperature field distribution matrix is ​​output, which is composed of the predicted temperature values ​​of each node within the set future step size.

[0009] Preferably, the step of calculating the deviation between the predicted temperature field distribution matrix and the target curing temperature curve to generate an error matrix includes: Slide the window according to the time step and extract the target temperature vector of each node within the time period corresponding to the future set step size on the target curing temperature curve. Calculate the difference between the predicted temperature value of the same node at the same time stamp in the predicted temperature field distribution matrix and the corresponding target temperature value in the target temperature vector; The differences between all nodes are matrix-reorganized according to the spatial arrangement order of the nodes in the spatial topology graph to generate the error matrix.

[0010] Preferably, the step of solving and outputting the power adjustment increment of each heating zone actuator by inverse dynamics model based on the error matrix includes: The inverse dynamics model is constructed using a long short-term memory network. Flatten the error matrix into a one-dimensional error vector; Obtain the historical power regulation increment sequence stored in the previous control cycle; The one-dimensional error vector is concatenated with the historical power adjustment increment sequence and then input into the long short-term memory network. A linear transformation is performed through the output layer of the long short-term memory network to output a one-dimensional power adjustment increment vector composed of the power adjustment increments corresponding to the actuators of each heating zone.

[0011] Preferably, after generating the spatial topology map, the method further includes: Missing data are detected in the real-time data collected by the multi-node temperature sensor; When the temperature data of the first target node is missing, the current temperature data of all second target nodes directly connected to the first target node in the spatial topology map are extracted. Based on the edge weights in the spatial topology graph, calculate the weight coefficient of the temperature data of the second target node relative to the first target node; The temperature data of the second target node is weighted and summed using the weighting coefficients to generate the estimated temperature data of the first target node and fill it into the multidimensional temperature sequence.

[0012] Preferably, inputting the multidimensional temperature sequence into the graph convolutional layer includes: Obtain the local density and local thickness values ​​of the sponge fibers corresponding to the location of the multi-node temperature sensor; The local thermal resistance coefficient between adjacent nodes is calculated using the local density value and the local thickness value. The local thermal resistance coefficient is constructed as an edge feature matrix corresponding to the number of edges of the nodes in the spatial topology graph. During the forward propagation of the graph convolutional layer, the edge feature matrix is ​​multiplied by the adjacency matrix of the spatial topology graph, and the product result is used as the message passing weight matrix of the graph convolutional layer.

[0013] Preferably, before inputting the joint feature matrix into the fully connected layer at the end of the spatiotemporal graph neural network model, the method further includes: A residual connection structure is introduced; the temporal lag feature output by the gated recurrent unit layer is dimensionally aligned with the spatiotemporal fusion feature vector output by the multi-head attention mechanism layer; The dimension-aligned temporal lag features are added element-wise to the spatiotemporal fusion feature vector to generate a residual feature matrix; The spatiotemporal fusion feature vector portion in the joint feature matrix is ​​replaced with the residual feature matrix to generate the updated joint feature matrix.

[0014] Preferably, the training process of the Long Short-Term Memory network includes: When the sponge fiber is offline, multiple sets of step power signals with different amplitudes are applied to the actuators of each heating zone in the heating furnace. Record the temperature response curves of each node of the multi-node temperature sensor under the step power signal; For each set of step power signals, the optimal power adjustment increment sequence is solved using the differential evolution algorithm, with the goal of minimizing the deviation between the temperature response curve of each node and the offline target curing temperature curve. The error data corresponding to the step power signal at the specified time and the optimal power adjustment increment sequence are used as sample pairs to train the long short-term memory network.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention constructs a spatial topology map by deploying multi-node temperature sensors within a heating furnace. The multidimensional temperature sequence is input into a spatiotemporal graph neural network to extract the spatial adjacency heat conduction characteristics and temporal lag characteristics between nodes, outputting a predicted temperature field distribution matrix for a predetermined future step size. Based on the deviation between this predicted matrix and the target curing curve, the power adjustment increment of each heating zone actuator is solved inversely using an inverse dynamics model. This, combined with real-time temperature feedback, forms a feedforward-feedback composite control closed loop. This invention transforms spatial physical topology and temporal lag characteristics into graph-structured data that the model can process, enabling pre-calculation of the future temperature distribution in unmeasured areas within the sponge fiber. This allows the control system to adjust the power of each heating zone in advance based on future deviations, overcoming the control lag phenomenon caused by the material's low thermal conductivity and avoiding local temperature overshoot and uneven curing.

[0016] 2. An adaptive degree centrality algorithm is introduced to calculate local connection weights when constructing the spatial topology graph, ensuring that the connection relationships between nodes closely match the actual heat conduction paths. To address missing sensor data, the current temperature data of adjacent nodes in the graph structure are used to perform weighted summation with edge weights to fill in the gaps, maintaining the integrity of the input data. During the forward propagation of the graph convolutional layer, the local thermal resistance coefficient is calculated by combining the local density and thickness of the sponge fiber and transformed into an edge feature matrix to participate in the Hadamard product, integrating material physical parameters into the spatial feature extraction process. Residual connections are set in the long short-term memory network structure to perform element-wise addition, alleviating the gradient vanishing problem in deep network training. During the training phase of the inverse dynamics model, a step power signal is applied to record the response curve, and the optimal power adjustment increment sequence is solved using a differential evolution algorithm as training samples, improving the accuracy of power calculation under complex temperature fields. Attached Figure Description

[0017] Figure 1 The flowchart below shows the overall method for optimizing the temperature control parameters of sponge fibers according to the present invention. Figure 2 This is a flowchart illustrating the construction of the spatial topology of the heating furnace temperature measurement network according to the present invention. Figure 3 This is a flowchart of the spatiotemporal feature extraction process of the spatiotemporal graph neural network of the present invention; Figure 4 This is a flowchart of the process for generating the predicted temperature field distribution matrix according to the present invention; Figure 5 This is a flowchart of the error matrix generation and power adjustment increment solution of the present invention; Figure 6 This is a flowchart of the sensor data missing compensation and graph convolution weight optimization process of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Please refer to Figure 1 This embodiment provides a data-driven method for optimizing temperature control parameters of sponge fibers. The heating furnace used for curing the sponge fibers is a continuous heating furnace. The interior of the heating furnace is divided into multiple independent heating zones along the direction of the sponge fiber's movement. Each heating zone is equipped with at least one set of independently controllable heating actuators. The heating actuators can adjust their output heating power through input power control signals. The internal cavity of the heating furnace has a regular structure. The sponge fibers pass through the heating furnace cavity at a uniform speed along the direction of movement in a flat state. The speed of the sponge fibers can be adjusted according to the curing process requirements.

[0020] A spatial topology map is constructed by deploying multi-node temperature sensors within the heating furnace. All temperature sensors maintain a consistent sampling period, which is matched to the furnace's control cycle. The multi-node temperature sensors cover the furnace's layout direction, width direction, and thickness direction, forming a three-dimensional temperature measurement network. Along the layout direction, sensor nodes are deployed at the inlet, middle, and outlet positions of each heating zone; along the width direction, sensor nodes are deployed at multiple lateral positions within the furnace cavity; and along the thickness direction, sensor nodes are deployed at positions corresponding to different thickness layers of the sponge fiber. The physical installation coordinates of all sensor nodes are calibrated and stored in the control system's storage unit after the furnace installation is completed. Based on the calibrated physical installation coordinates of all sensor nodes, a spatial topology map of the furnace's temperature measurement network is constructed. Nodes in the spatial topology map correspond to each temperature sensor, and the edges of the spatial topology map correspond to the heat conduction relationships between nodes.

[0021] During the curing process of the sponge fiber, all temperature sensors synchronously collect temperature data according to a preset sampling period, generating a real-time multidimensional temperature sequence. Each row of the multidimensional temperature sequence corresponds to a sensor node, and each column corresponds to a sampling timestamp. Each element in the sequence is the measured temperature value of the corresponding node at the corresponding timestamp. The real-time collected multidimensional temperature sequence is input into a pre-trained spatiotemporal graph neural network (SPNN). The SPNN is used to extract the spatial adjacency heat conduction features and temporal lag features between nodes. The SPNN consists of a graph convolutional layer, a gated recurrent unit layer, and a multi-head attention mechanism layer connected in sequence. The graph convolutional layer aggregates the spatial features in the multidimensional temperature sequence and extracts the heat conduction features between nodes based on spatial adjacency. The gated recurrent unit layer models the temporal dimension of the spatial features output by the graph convolutional layer, capturing the temporal lag characteristics during temperature changes. The multi-head attention mechanism layer performs global correlation modeling on the temporal features output by the gated recurrent unit layer, assigning attention weights to the temporal features of different nodes, and finally outputting a spatiotemporal fusion feature vector.

[0022] Using a trained spatiotemporal graph neural network model, a predicted temperature field distribution matrix is ​​output for a future set time step. The future set time step is determined based on the control cycle of the heating furnace and the lag time of heat conduction in the sponge fiber, ensuring that the total duration corresponding to the set time step is not less than the lag time of heat conduction in the sponge fiber within the heating furnace. The current power input sequence of the actuators in each heating zone of the heating furnace is obtained. This current power input sequence contains the output power values ​​of each actuator within a set number of past control cycles. The current power input sequence is concatenated with the spatiotemporal fusion feature vector along the feature dimension to generate a joint feature matrix. This joint feature matrix is ​​input into the fully connected layer at the end of the spatiotemporal graph neural network model. The fully connected layer performs a nonlinear mapping on the joint feature matrix, outputting a predicted temperature field distribution matrix composed of the predicted temperature values ​​of each node within the future set time step. The rows of the predicted temperature field distribution matrix correspond to the future time step, the columns correspond to the sensor nodes, and each element in the matrix is ​​the predicted temperature value of the corresponding node at the corresponding time step.

[0023] The deviation between the predicted temperature field distribution matrix and the target curing temperature curve is calculated to generate an error matrix. The target curing temperature curve is a temperature-time curve corresponding to each sensor node location, pre-set according to the curing process requirements of the sponge fiber. The target curing temperature curve is stored in the storage unit of the control system and can be updated according to the material, thickness, and fabric feeding speed of the sponge fiber. A sliding window is used to extract the target temperature vector of each node within the time period corresponding to the future set step size from the target curing temperature curve. The difference between the predicted temperature value of the same node at the same timestamp in the predicted temperature field distribution matrix and the corresponding target temperature value in the target temperature vector is calculated. The differences of all nodes are then matrix-reorganized according to the spatial arrangement order of the nodes in the spatial topology graph to generate the error matrix.

[0024] The power adjustment increment of each heating zone actuator is solved and output by inverse dynamics model based on the error matrix. The inverse dynamics model is constructed using a long short-term memory network and pre-trained offline to establish a nonlinear mapping relationship between temperature error and heating actuator power adjustment increment. The error matrix is ​​flattened into a one-dimensional error vector, and the historical power adjustment increment sequence stored in the previous control cycle is obtained. The one-dimensional error vector and the historical power adjustment increment sequence are concatenated and input into the long short-term memory network. A linear transformation is performed through the output layer of the long short-term memory network to output a one-dimensional power adjustment increment vector composed of the power adjustment increments corresponding to each heating zone actuator.

[0025] The power adjustment increment is superimposed on the current power base and sent to the actuators of each heating zone. The current power base is the output power value sent to the corresponding actuator in the previous control cycle. Each heating zone actuator adjusts its output heating power according to the superimposed power command. Simultaneously, multi-node temperature sensors continuously collect real-time temperature data, which is used as feedback input to the control system. This data is compared with the predicted temperature field distribution matrix to update the input sequence of the spatiotemporal graph neural network, forming a feedforward-feedback composite control closed loop. The feedforward control link generates the power adjustment increment in advance based on the predicted deviation of the future temperature field, achieving proactive intervention in temperature changes. The feedback control link corrects the input of the prediction model based on the real-time collected temperature data, ensuring the steady-state accuracy of temperature field control. The composite control closed loop formed by the combination of the two can simultaneously take into account the proactive nature and steady-state accuracy of the control.

[0026] Table 1 Mapping Relationship between Heating Zones and Temperature Sensor Nodes in Heating Furnace ; Table 1 shows the mapping relationship between heating zones and temperature sensor nodes in the heating furnace. This table clarifies the spatial correspondence between actuators and temperature sensor nodes in each heating zone, providing a spatial mapping basis for the construction of spatial topology, spatial aggregation of heat conduction characteristics, and partition allocation of power regulation increments. It ensures the spatial matching between control commands and temperature feedback, and avoids misalignment between the power regulation area and the temperature monitoring area.

[0027] In this embodiment, a spatial topology map constructed by multi-node temperature sensors is used to transform the three-dimensional temperature field inside the heating furnace into graph structure data. Spatial correlation features and temporal lag features of heat conduction are extracted synchronously through a spatiotemporal graph neural network, enabling a forward prediction of the future temperature field distribution. Based on the predicted temperature deviation, the power adjustment increment is solved in reverse. Combined with real-time temperature feedback, a feedforward-feedback composite control closed loop is formed, realizing the advanced control of the temperature field of the heating furnace. This overcomes the control lag problem caused by the low thermal conductivity of sponge fibers and avoids temperature overshoot and uneven curing during the curing process.

[0028] In a preferred embodiment, reference Figure 2 The physical installation coordinates of the multi-node temperature sensors within the heating furnace are obtained. These coordinates are calibrated using a three-dimensional Cartesian coordinate system, with the origin set as the reference vertex at the furnace cavity inlet. The X-axis extends along the width of the furnace, the Y-axis along the furnace's layout direction, and the Z-axis along the furnace's height. The physical installation coordinates of each sensor node are calibrated as three-dimensional coordinate values ​​and stored. Based on these physical installation coordinates, the Euclidean distance between each pair of nodes is calculated, generating an initial distance matrix. The matrix is ​​a square matrix, where N is the total number of sensor nodes. The element in the i-th row and j-th column of the initial distance matrix is ​​the Euclidean distance between node i and node j. The formula for calculating the Euclidean distance is: in, Let be the Euclidean distance between node i and node j. Let node i be the three-dimensional physical coordinate. The three-dimensional physical installation coordinates of node j.

[0029] A preset distance threshold is set, which is determined based on the thermal conductivity of the sponge fibers in the heating furnace and the node density. Node pairs in the initial distance matrix whose Euclidean distance is less than the preset distance threshold are marked as adjacent nodes, generating an initial adjacency matrix. The initial adjacency matrix is... The initial adjacency matrix is ​​a square matrix where adjacent nodes have values ​​of 1 and non-adjacent nodes have values ​​of 0. An adaptive degree centrality algorithm is introduced to calculate the local connection weights of each node. These weights are then used to update the edge weights in the initial adjacency matrix, generating a spatial topology graph. Degree centrality is the number of direct neighbors a node has in the spatial topology graph, representing the centrality of a node in the temperature measurement network. The degree centrality of node i is... The calculation method is the sum of all elements in the i-th row of the initial adjacency matrix. The edge weights between nodes are calculated based on degree centrality, using the following formula: in, Let be the edge weight between node i and node j. Let i be the degree centrality. Let j be the degree centrality. For the maximum degree centrality of all nodes in the spatial topological graph, This is an indicator function that takes the value 1 when the condition within the parentheses is true, and 0 otherwise. A preset distance threshold is used. In the adjacency matrix updated in this way, the edge weights are positively correlated with the centrality of the nodes, so that nodes located at the center of the temperature measurement network have higher connection weights. This closely matches the actual path of heat conduction from the center to the surrounding areas in the heating furnace, avoiding the problem that a fixed adjacency matrix cannot adapt to the differences in the spatial distribution of heat conduction.

[0030] refer to Figure 6 After generating the spatial topology graph, missing data detection is performed on the real-time data collected by the multi-node temperature sensors. A threshold-based method is used for missing data detection. When the sampled data of a sensor node exceeds the preset temperature measurement range, or when no valid data is uploaded for multiple consecutive sampling periods, the node is determined to have missing temperature data and is marked as the first target node. When missing temperature data is detected for the first target node, the current temperature data of all second target nodes directly connected to the first target node in the spatial topology graph is extracted. The second target nodes are the nodes in the initial adjacency matrix whose corresponding element is 1. Based on the edge weights in the spatial topology graph, the weight coefficient of the temperature data of the second target node relative to the first target node is calculated. The weight coefficient is the proportion of the edge weight between the second target node and the first target node to the sum of the edge weights between all second target nodes and the first target node. The temperature data of the second target nodes is weighted and summed using the weight coefficient to generate the estimated temperature data of the first target node and fill it into the multidimensional temperature sequence. The formula for the weighted summation is: in, The estimated temperature data for the first target node m with missing data. Let be the set of all second target nodes n that are directly connected to node m in the spatial topology graph. Let be the edge weight between node m and node n. This represents the current temperature data for node n. This method allows for data filling based on measured data from adjacent nodes and heat conduction correlation weights when data from one or more sensor nodes is missing. This maintains the integrity of the multidimensional temperature sequence, ensures the continuity of input data to the spatiotemporal graph neural network, and avoids feature extraction bias and control inaccuracies caused by missing data.

[0031] When the multidimensional temperature sequence is input into the graph convolutional layer, the local density and thickness values ​​of the sponge fiber corresponding to the location of the multi-node temperature sensor are obtained. These local density and thickness values ​​are synchronously detected by an online detection device before the sponge fiber enters the heating furnace. The detection data is linked to the sponge fiber's path. When the sponge fiber reaches the corresponding sensor node position, the corresponding local density and thickness values ​​are synchronously input into the control system. The local thermal resistance coefficient between adjacent nodes is calculated using the local density and thickness values. The formula for calculating the local thermal resistance coefficient is: in, Let be the local thermal resistance coefficient between node i and node j. The average thickness of the sponge fiber between node i and node j is obtained by averaging the local thickness values ​​at corresponding positions of nodes i and j. The average thermal conductivity of the sponge fibers between node i and node j is calculated from the local density values ​​at corresponding positions of node i and node j using a preset density-thermal conductivity mapping relationship. The effective cross-sectional area for heat conduction between node i and node j is calculated from the node spacing and the thickness of the sponge fiber. The local thermal resistance coefficient is constructed as an edge feature matrix corresponding to the number of edges of the nodes in the spatial topology graph. The edge feature matrix is ​​an N×N square matrix, where the element in the i-th row and j-th column is the reciprocal of the local thermal resistance coefficient between node i and node j, used to characterize the heat conduction capability between nodes. During the forward propagation of the graph convolutional layer, the edge feature matrix and the adjacency matrix of the spatial topology graph are multiplied by a Hadamard product, and the result is used as the message passing weight matrix of the graph convolutional layer. The forward propagation calculation formula for the graph convolutional layer is: in, This is the output feature matrix of the (l+1)th graph convolutional layer. It is a non-linear activation function. The weighted adjacency matrix for adding self-loops, where A is the adjacency matrix of the spatial topological graph and M is the edge feature matrix. This is the Hadamard product operation, where I is the identity matrix. for The corresponding degree matrix, Let l be the input feature matrix of the l-th graph convolutional layer. Let L be the trainable weight matrix of the l-th graph convolutional layer. This is the bias vector of the l-th graph convolutional layer. By incorporating the local physical parameters of the sponge fiber into the message passing process of the graph convolutional layer, the spatial feature extraction process closely matches the actual thermal conductivity characteristics of the sponge fiber, improving the extraction accuracy of spatially adjacent thermal conductivity features and avoiding the problem that general graph convolutional layers cannot adapt to differences in material physical properties.

[0032] Table 2. Sensor Node Adjacency Relationships and Edge Weight Parameters ; Table 2 shows the adjacency relationship and edge weight parameters of sensor nodes. This table quantifies the adjacency relationship, connection weight and thermal conductivity parameters of each node in the spatial topology graph. It provides a direct quantitative basis for the calculation of message passing weights in graph convolutional layers and the weighted imputation of missing data, ensuring the accuracy of spatial feature extraction and data imputation processes, and realizing the deep binding of thermal conductivity characteristics and graph structure modeling.

[0033] In this embodiment, the edge weights of the spatial topology graph are optimized by an adaptive degree centrality algorithm, so that the connection relationship between nodes closely matches the actual heat conduction path inside the heating furnace; missing data is filled by weighted summation of adjacent nodes, ensuring the integrity of the input data; by converting the local density and thickness of the sponge fiber into the local thermal resistance coefficient and incorporating it into the forward propagation process of the graph convolutional layer, the extraction accuracy of spatial heat conduction features is improved, further enhancing the spatiotemporal graph neural network's ability to model the temperature field.

[0034] In a preferred embodiment, reference Figure 3 The spatiotemporal graph neural network comprises sequentially connected graph convolutional layers, gated recurrent unit layers, and multi-head attention mechanism layers. A multidimensional temperature sequence is input into the graph convolutional layers, where node features are aggregated based on edge weights in the spatial topology graph, outputting spatially adjacent heat conduction features. The output features from multiple graph convolutional layers are concatenated along the channel dimension to generate the final spatially adjacent heat conduction features. These features are then input into the gated recurrent unit layers, where update and reset gates control the retention and forgetting of historical temporal information, outputting temporally lagging features. The formula for calculating the update gate of the gated recurrent unit is as follows: in, Let be the update gate output at time t. To update the gate weight matrix, The hidden layer state at time t-1 The input feature at time t is the spatial adjacency heat conduction feature. To update the bias vector of the gate.

[0035] The formula for calculating the reset door of the gated loop unit is: in, The reset gate output at time t. To reset the weight matrix of the gate, This is the offset vector for resetting the gate.

[0036] The formula for calculating the candidate hidden state of a gated loop unit is: in, Let be the candidate hidden state at time t. Let be the weight matrix of the candidate hidden states. For Hadamard product operation, is the bias vector of the candidate hidden state.

[0037] The formula for calculating the hidden state update of the gated loop unit is: in, Let t be the output hidden state at time t, representing the time-series lag characteristic. Through the gating mechanism of the gated recurrent unit, long-term time-series dependencies in the temperature change process can be effectively captured, distinguishing between effective and redundant information in historical time-series data, and accurately extracting the time-series lag characteristics in the heat conduction process of sponge fibers, thus avoiding the problem that traditional time-series models cannot effectively capture long-lag characteristics.

[0038] The temporal lag features are input into the multi-head attention mechanism layer, and global attention weights are assigned to the temporal lag features at different nodes, outputting a spatiotemporal fusion feature vector. The multi-head attention mechanism layer contains multiple independent attention heads, each corresponding to an independent linear transformation weight matrix, enabling correlation modeling of temporal lag features from different feature subspaces. The output calculation formula of the multi-head attention mechanism is as follows: in, The output of the multi-head attention mechanism is represented by Q, K, and V, which are the query matrix, key matrix, and value matrix, respectively, all obtained by linear transformation of temporal lag features. h represents the number of attention heads. , , Let be the linear transformation weight matrices of the query, key, and value corresponding to the i-th attention head. Let be the dimension of the key matrix. This is the linear transformation weight matrix of the multi-head attention output. Through the multi-head attention mechanism, the focus on key node features that are significantly affected by temperature field changes can be strengthened, the interference of redundant node features can be suppressed, and deep fusion of spatial and temporal features can be achieved, thus improving the effectiveness of feature representation.

[0039] refer to Figure 4 Before inputting the joint feature matrix into the fully connected layer at the end of the spatiotemporal graph neural network model, a residual connection structure is introduced. The temporal lag features output from the gated recurrent unit layer and the spatiotemporal fusion feature vector output from the multi-head attention mechanism layer are dimensionally aligned using a linear transformation layer, mapping the temporal lag features and the spatiotemporal fusion feature vector to the same feature dimension. The dimension-aligned temporal lag features and the spatiotemporal fusion feature vector are then added element-wise to generate a residual feature matrix. This residual feature matrix is ​​then used to replace the spatiotemporal fusion feature vector portion of the joint feature matrix, generating an updated joint feature matrix. Through the residual connection structure, the temporal lag features from the lower layers can be directly passed to the deeper layers of the network, alleviating the gradient vanishing problem during deep network training and improving the training convergence speed and prediction accuracy of the spatiotemporal graph neural network.

[0040] The current power input sequence of each heating zone actuator in the heating furnace is obtained. The length of the current power input sequence is consistent with the sampling length of the multidimensional temperature sequence, and includes the output power values ​​of each heating zone actuator within multiple past sampling periods. The current power input sequence and the residual feature matrix are concatenated along the feature dimension to generate a joint feature matrix. Each row of the joint feature matrix corresponds to a sampling timestamp, and each column corresponds to a feature dimension, which includes node temperature features and actuator power features. The joint feature matrix is ​​input into the fully connected layer at the end of the spatiotemporal graph neural network model. Multiple fully connected layers perform a progressively nonlinear mapping on the joint feature matrix, outputting a predicted temperature field distribution matrix composed of the predicted temperature values ​​of each node within a set future step size.

[0041] refer to Figure 5 The deviation between the predicted temperature field distribution matrix and the target curing temperature curve is calculated to generate an error matrix. A sliding window is used to extract the target temperature vectors for each node within a time period corresponding to a future set step size on the target curing temperature curve. The length of the target temperature vector is the same as the total number of sensor nodes, and each element in the vector is the target temperature value of the corresponding node at the corresponding timestamp. The difference between the predicted temperature value of the same node at the same timestamp in the predicted temperature field distribution matrix and the corresponding target temperature value in the target temperature vector is calculated using the following formula: in, Let be the temperature error value of the p-th node at the t-th prediction time step. Let be the predicted temperature value of the p-th node at the t-th prediction time step. Let be the target temperature value corresponding to the p-th node at the t-th prediction time step. The differences between all nodes are matrix-reorganized according to the spatial arrangement of the nodes in the spatial topology graph to generate an error matrix. The rows of the error matrix correspond to the prediction time steps, the columns correspond to the sensor nodes, and each element in the matrix is ​​the temperature error value of the corresponding node at the corresponding time step.

[0042] Based on the error matrix, the power adjustment increment of each heating zone actuator is solved inversely using an inverse dynamics model, which is then output as the inverse dynamics model. This model employs a Long Short-Term Memory (LSTM) network, which includes an input layer, multiple LSM layers, and a fully connected output layer. The error matrix is ​​flattened into a one-dimensional error vector, the length of which is the product of the number of prediction time steps and the total number of sensor nodes. The historical power adjustment increment sequence stored in the previous control cycle is obtained, with a length equal to the preset number of historical cycles, containing the power adjustment increment values ​​of each heating zone actuator over multiple past control cycles. The one-dimensional error vector is concatenated with the historical power adjustment increment sequence and then input into the LSM network. The cell state update calculation formula for the LSM network is as follows: in, Let t represent the cell state at time t. The output of the forget gate at time t. The cell state at time t-1. Let be the input gate output at time t, and be the candidate cell state at time t. The spliced ​​input sequence is time-series modeled using multiple hidden layers of a Long Short-Term Memory (LSTM) network to capture the dynamic mapping relationship between temperature error and power regulation increment. A linear transformation is performed through the output layer of the LSM network to output a one-dimensional power regulation increment vector composed of the power regulation increments corresponding to the actuators of each heating zone.

[0043] The training process of the Long Short-Term Memory (LSTM) network was completed in an offline state with sponge fibers. The offline state was either an unloaded state with no sponge fibers running inside the heating furnace, or a static testing state with standard test sponge fibers laid inside. Multiple sets of step power signals with different amplitudes were applied to the actuators in each heating zone of the heating furnace. The amplitude of the step power signals covered the set range of the actuator's rated power. The duration of each set of step power signals was not less than the thermal equilibrium time of the heating furnace temperature field, and the interval between two adjacent sets of step power signals was not less than the time it took for the heating furnace temperature field to recover to its initial state. The temperature response curves of each node of the multi-node temperature sensor under the step power signals were recorded. The sampling period of the temperature response curves was consistent with the sampling period of the online control process. The measured temperature value of each node was recorded at each sampling timestamp. For each set of step power signals, the optimal power adjustment increment sequence was solved using a differential evolutionary algorithm, with the optimization objective being minimizing the deviation between the temperature response curve of each node and the offline target curing temperature curve. The fitness function calculation formula for the differential evolutionary algorithm is as follows: in, For the fitness function value, For power adjustment increment sequence, Let be the total time step of the temperature response curve, and be the total number of sensor nodes. To apply power adjustment increment sequence The measured temperature value of the p-th node at the t-th time step is used as the optimization objective, which is to minimize the fitness function value. After iterative solution, the power adjustment increment sequence with the minimum fitness function value is output as the optimal power adjustment increment sequence. The error data corresponding to the step power signal at each time step and the optimal power adjustment increment sequence are used as sample pairs to construct a training dataset. The training dataset is divided into a training set and a validation set according to a set ratio. The long short-term memory network is trained using the training set, and the accuracy of the trained model is verified using the validation set. The model training is completed when the loss function value of the validation set is lower than a preset threshold.

[0044] Table 3. Parameter Configuration Table for Inverse Dynamics Model Training Samples ; Table 3 shows the parameter configuration table for training samples of the inverse dynamics model. This table standardizes the input parameters of the step power signal, the optimized solution configuration, and the sample pair construction rules during offline training. It provides standardized sample data for the training of the long short-term memory network, ensuring the convergence of the inverse dynamics model and the accuracy of the power solution, and avoiding the solution deviation of the model in different power ranges.

[0045] In this embodiment, the deep fusion of spatiotemporal features is achieved by combining a gated recurrent unit with a multi-head attention mechanism. The gradient vanishing problem of deep networks is alleviated by the residual connection structure, which improves the accuracy of temperature field prediction. An inverse dynamics model is constructed by a long short-term memory network, which enables accurate reverse solving from temperature error to power adjustment increment. The optimal power sequence is solved by offline step testing and differential evolution algorithm, which builds a high-quality training sample set, improves the solution accuracy of the inverse dynamics model under complex temperature fields, and further optimizes the control performance of the feedforward-feedback composite control closed loop.

Claims

1. A data-driven method for optimizing temperature control parameters of sponge fibers, characterized in that, include: A spatial topology map is constructed by deploying multi-node temperature sensors inside the heating furnace. The real-time acquired multidimensional temperature sequence is input into the spatiotemporal graph neural network to extract the spatial adjacency heat conduction characteristics and temporal lag characteristics between nodes; The trained spatiotemporal neural network model is used to output the predicted temperature field distribution matrix for a future set step size; The deviation between the predicted temperature field distribution matrix and the target curing temperature curve is calculated to generate an error matrix; Based on the error matrix, the power adjustment increment of each heating zone actuator is obtained by inversely solving the problem using the inverse dynamics model. The power adjustment increment is added to the current power base and sent to the actuators of each heating zone, forming a feedforward-feedback composite control closed loop in combination with real-time temperature feedback.

2. The data-driven method for optimizing temperature control parameters of sponge fibers according to claim 1, characterized in that, The method of constructing a spatial topology map by deploying multi-node temperature sensors within the heating furnace includes: Obtain the physical installation coordinates of the multi-node temperature sensor within the heating furnace; Calculate the Euclidean distance between each pair of nodes based on the physical installation coordinates and generate an initial distance matrix; Set a preset distance threshold, mark the nodes in the initial distance matrix whose Euclidean distance is less than the preset distance threshold as adjacent nodes, and generate an initial adjacency matrix; An adaptive degree centrality algorithm is introduced to calculate the local connection weights of each node, and the edge weights in the initial adjacency matrix are updated using the local connection weights to generate the spatial topology graph.

3. The data-driven method for optimizing temperature control parameters of sponge fibers according to claim 1, characterized in that, The step of inputting the real-time acquired multidimensional temperature sequence into a spatiotemporal graph neural network to extract spatial adjacency heat conduction features and temporal lag features between nodes includes: The spatiotemporal graph neural network includes a graph convolutional layer, a gated recurrent unit layer, and a multi-head attention mechanism layer connected in sequence. The multidimensional temperature sequence is input into the graph convolutional layer, and the node features are aggregated based on the edge weights in the spatial topology graph to output the spatial adjacency heat conduction features. The spatial adjacency heat conduction feature is input into the gated loop unit layer, and the retention and forgetting of historical time sequence information are controlled by the update gate and the reset gate, and the time sequence lag feature is output. The temporal lag features are input into the multi-head attention mechanism layer, and global attention weights are assigned to the temporal lag features of different nodes, outputting a spatiotemporal fusion feature vector.

4. The data-driven method for optimizing temperature control parameters of sponge fibers according to claim 3, characterized in that, The method of using the trained spatiotemporal graph neural network model to output a predicted temperature field distribution matrix for a future set step size includes: Obtain the current power input sequence of the actuators in each heating zone of the heating furnace; The current power input sequence and the spatiotemporal fusion feature vector are concatenated along the feature dimension to generate a joint feature matrix; The joint feature matrix is ​​input into the fully connected layer at the end of the spatiotemporal graph neural network model; The joint feature matrix is ​​nonlinearly mapped by the fully connected layer, and the predicted temperature field distribution matrix is ​​output, which is composed of the predicted temperature values ​​of each node within the set future step size.

5. The data-driven method for optimizing temperature control parameters of sponge fibers according to claim 1, characterized in that, The step of calculating the deviation between the predicted temperature field distribution matrix and the target curing temperature curve to generate an error matrix includes: Slide the window according to the time step and extract the target temperature vector of each node within the time period corresponding to the future set step size on the target curing temperature curve. Calculate the difference between the predicted temperature value of the same node at the same time stamp in the predicted temperature field distribution matrix and the corresponding target temperature value in the target temperature vector; The differences between all nodes are matrix-reorganized according to the spatial arrangement order of the nodes in the spatial topology graph to generate the error matrix.

6. The data-driven method for optimizing temperature control parameters of sponge fibers according to claim 1, characterized in that, The process of solving and outputting the power adjustment increment of each heating zone actuator based on the error matrix using an inverse dynamics model includes: The inverse dynamics model is constructed using a long short-term memory network. Flatten the error matrix into a one-dimensional error vector; Obtain the historical power regulation increment sequence stored in the previous control cycle; The one-dimensional error vector is concatenated with the historical power adjustment increment sequence and then input into the long short-term memory network. A linear transformation is performed through the output layer of the long short-term memory network to output a one-dimensional power adjustment increment vector composed of the power adjustment increments corresponding to the actuators of each heating zone.

7. The data-driven method for optimizing temperature control parameters of sponge fibers according to claim 2, characterized in that, After generating the spatial topology map, the process further includes: Missing data are detected in the real-time data collected by the multi-node temperature sensor; When the temperature data of the first target node is missing, the current temperature data of all second target nodes directly connected to the first target node in the spatial topology map are extracted. Based on the edge weights in the spatial topology graph, calculate the weight coefficient of the temperature data of the second target node relative to the first target node; The temperature data of the second target node is weighted and summed using the weighting coefficients to generate the estimated temperature data of the first target node and fill it into the multidimensional temperature sequence.

8. The data-driven method for optimizing temperature control parameters of sponge fibers according to claim 3, characterized in that, The step of inputting the multidimensional temperature sequence into the graph convolutional layer includes: Obtain the local density and local thickness values ​​of the sponge fibers corresponding to the location of the multi-node temperature sensor; The local thermal resistance coefficient between adjacent nodes is calculated using the local density value and the local thickness value. The local thermal resistance coefficient is constructed as an edge feature matrix corresponding to the number of edges of the nodes in the spatial topology graph. During the forward propagation of the graph convolutional layer, the edge feature matrix is ​​multiplied by the adjacency matrix of the spatial topology graph, and the product result is used as the message passing weight matrix of the graph convolutional layer.

9. The data-driven method for optimizing temperature control parameters of sponge fibers according to claim 4, characterized in that, Before inputting the joint feature matrix into the fully connected layer at the end of the spatiotemporal graph neural network model, the method further includes: A residual connection structure is introduced; the temporal lag feature output by the gated recurrent unit layer is dimensionally aligned with the spatiotemporal fusion feature vector output by the multi-head attention mechanism layer; The dimension-aligned temporal lag features are added element-wise to the spatiotemporal fusion feature vector to generate a residual feature matrix; The spatiotemporal fusion feature vector portion in the joint feature matrix is ​​replaced with the residual feature matrix to generate the updated joint feature matrix.

10. The data-driven method for optimizing temperature control parameters of sponge fibers according to claim 6, characterized in that, The training process of the Long Short-Term Memory network includes: When the sponge fiber is offline, multiple sets of step power signals with different amplitudes are applied to the actuators of each heating zone in the heating furnace. Record the temperature response curves of each node of the multi-node temperature sensor under the step power signal; For each set of step power signals, the optimal power adjustment increment sequence is solved using the differential evolution algorithm, with the goal of minimizing the deviation between the temperature response curve of each node and the offline target curing temperature curve. The error data corresponding to the step power signal at the specified time and the optimal power adjustment increment sequence are used as sample pairs to train the long short-term memory network.

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