Low-alloy steel castings hot spot position prediction method based on bayesian dynamic inference graph

Abstract

This invention discloses a method for predicting the location of hot spots in low-alloy steel castings based on a Bayesian dynamic inference graph. The method includes: acquiring a three-dimensional digital model of the low-alloy steel casting and forming a set of nodes for a central axis transformation skeleton; generating a physical feature matrix of candidate nodes; establishing an initial topological skeleton graph structure based on the set of nodes for the central axis transformation skeleton and their connectivity; extracting a set of causal relationships between nodes using an improved NOTEARS continuous optimization method; constructing a set of Bayesian posterior physical constraint rules, leading to an optimized directed acyclic graph causal weight matrix and an updated set of causal relationships between nodes; and displaying the corresponding spatial location of the hot spot in the three-dimensional digital model of the low-alloy steel casting, thus completing the prediction of the hot spot location. This invention ensures that the hot spot prediction results closely match the actual casting defect generation mechanism, significantly reducing misjudgments and omissions in multiple complex process scenarios, and improving the accuracy and engineering applicability of intelligent identification.

Description

Technical Field

[0001] This invention relates to the field of metal technology, and in particular to a method for predicting the location of hot spots in low-alloy steel castings based on Bayesian dynamic inference graphs. Background Technology

[0002] With the development of intelligent manufacturing technology, low alloy steel castings are increasingly widely used in heavy-duty equipment, engineering structures and key industrial components. Due to the complex structure of the castings, uneven wall thickness and uncontrollable feeding path, hot spot problems have become the key cause of shrinkage cavities and porosity defects.

[0003] The industry generally uses the modular method or thermal simulation method based on Chvorinov's law to determine hot spots. The modular method infers solidification time by the ratio of local geometric dimensions, ignoring the topology and causal dependence of the internal feeding channels of the casting, which is prone to misjudgment. Although the finite element thermal simulation method can obtain the temperature field evolution process, it has high computational complexity and is highly sensitive to mesh quality and boundary conditions, making it difficult to achieve fast and real-time hot spot location.

[0004] Some studies have attempted to introduce Bayesian networks to model hot spots using reasoning, predicting the final feeding region by utilizing the causal structure between nodes. However, traditional Bayesian network learning requires a combined search of all directed edges between node pairs. As the number of skeleton nodes increases, the search space grows exponentially, easily getting trapped in local optima and failing to provide a fast response in practical casting design. Furthermore, it often overlooks the actual physical laws existing in low-alloy steel castings, including the directionality of feeding driven by gravity, the solidification sequence controlled by modulus, and the differences in feeding resistance, resulting in a lack of physical interpretability and engineering reliability in the reasoning results. Summary of the Invention

[0005] One objective of this invention is to propose a method for predicting the location of hot spots in low-alloy steel castings based on Bayesian dynamic inference graphs. This invention enables the hot spot prediction results to closely match the actual casting defect generation mechanism, significantly reducing misjudgments and omissions in multiple complex process scenarios, and improving the accuracy and engineering applicability of intelligent identification.

[0006] A method for predicting the location of hot spots in low-alloy steel castings based on a Bayesian dynamic inference graph, according to an embodiment of the present invention, includes: A three-dimensional digital model of a low-alloy steel casting is acquired and a layered central axis transformation is performed to obtain central axis transformation skeleton data. Based on the central axis transformation skeleton data, bifurcation points, endpoints and geometric gradient abrupt change points are extracted to form a set of central axis transformation skeleton nodes. For the set of skeleton nodes of the central axis transformation, construct the corresponding physical feature vectors, and combine all physical feature vectors to generate the physical feature matrix of candidate nodes; An initial topological skeleton graph structure is established based on the set of nodes of the central axis transformation skeleton and their connectivity relationships; An improved NOTEARS continuous optimization method is adopted, which takes the initial topological skeleton graph structure as input, generates an initial directed acyclic graph causal weight matrix, and extracts the set of causal relationships between nodes. Construct a set of Bayesian posterior physical constraint rules, embed the set of Bayesian posterior physical constraint rules as a penalty term into the NOTEARS optimization objective, and perform constraint optimization on the initial directed acyclic graph causal weight matrix and the set of causal relationships between nodes to obtain the optimized directed acyclic graph causal weight matrix and the updated set of causal relationships between nodes. A causal chain is generated based on the updated set of causal relationships between nodes. The risk score of the causal chain is calculated by combining it with the optimized causal weight matrix of the directed acyclic graph, and a set of candidate skeleton nodes for hotspots is formed. The candidate skeleton node set of hot spots is mapped back to the three-dimensional digital model of the low alloy steel casting to obtain the spatial location data of the hot spots. The corresponding spatial location of the hot spots is then displayed in the three-dimensional digital model of the low alloy steel casting, thus completing the prediction of the hot spot location of the low alloy steel casting.

[0007] Optionally, the extraction of bifurcation points, endpoints, and geometric gradient abrupt change points based on the central axis transformation skeleton data includes: A 3D scanning device was used to acquire the surface and internal geometry of the target low-alloy steel casting to obtain a 3D digital model of the low-alloy steel casting. The three-dimensional digital model of the low alloy steel casting is subjected to skeleton extraction processing based on layered central axis transformation to obtain central axis transformation skeleton data; Spatial structure analysis is performed on the central axis transformation skeleton data to calculate the connection relationship between each skeleton point. Based on the connection relationship between each skeleton point, a skeleton connection graph structure is constructed, and a central axis transformation skeleton topology network is formed from the skeleton connection graph structure. Based on the central axis transformation skeleton topology network, the set of bifurcation point nodes, the set of endpoint nodes, and the set of geometric gradient abrupt change points are identified; The set of bifurcation point nodes, the set of endpoint nodes, and the set of geometric gradient mutation points are merged and deduplicated to form the set of central axis transformation skeleton nodes.

[0008] Optionally, constructing the corresponding physical feature vector for the set of central axis transformation skeleton nodes includes: For each skeleton node in the set of skeleton nodes for the central axis transformation, obtain the three-dimensional spatial coordinates of the corresponding skeleton node, and calculate the local modulus of the skeleton node based on the three-dimensional spatial coordinates of the skeleton node. For each skeleton node in the set of central axis transformation skeleton nodes, perform skeleton path search in the central axis transformation skeleton topology network to obtain the skeleton path distance from the skeleton node to the nearest riser; For each skeleton node in the central axis transformation skeleton node set, a region allocation method based on three-dimensional Voronoi space partitioning is adopted to divide the three-dimensional digital model of the low alloy steel casting into multiple node regions, and the control volume of the node region of each skeleton node is calculated. Based on the local modulus, skeleton path distance, and control volume, the three types of physical parameters of each skeleton node are combined to construct a physical feature vector. The physical feature vectors of all skeleton nodes are combined in the order of node index to generate a candidate node physical feature matrix.

[0009] Optionally, establishing the initial topology skeleton graph structure includes: For each skeleton node in the set of skeleton nodes in the central axis transformation, each skeleton node in the set of skeleton nodes in the central axis transformation is treated as a graph node, and any pair of skeleton nodes with a direct connected edge relationship is treated as a graph edge, thus constructing the node set and edge set of the initial topological skeleton graph structure. Assign a unique node index number to each skeleton node in the initial topology skeleton graph structure to form an initial topology skeleton graph structure identified by the node index number; The adjacency representation of the initial topological skeleton graph structure is constructed based on the node index number; Each row of physical feature vectors in the candidate node physical feature matrix is ​​associated with the corresponding skeleton node in the initial topology skeleton graph structure according to the node index number, forming an initial topology skeleton graph structure with physical feature annotations.

[0010] Optionally, the improved NOTEARS continuous optimization method includes: The NOTEARS optimization variable is set as a directed weighted adjacency matrix. The directed weighted adjacency matrix is ​​masked according to the adjacency relation matrix of the initial topology skeleton graph structure to obtain the masked directed weighted adjacency matrix. Combining the feeding channel characteristics of low alloy steel castings, a feasible feeding instruction matrix is ​​constructed based on the physical feature matrix of candidate nodes. Then, based on the feasible feeding instruction matrix, the mask constraint directed weighted adjacency matrix is ​​weighted at the element level to obtain the physical prior precondition weighted adjacency matrix. Construct a feed impedance matrix, where each element measures the difficulty of feeding in a certain direction. Construct a directional weighting matrix, use the directional weighting matrix to weight the physical prior precondition weighted adjacency matrix, and define the directional weighting acyclic constraint to obtain the directional directed acyclic constraint; A physical consistency multi-objective residual function is defined by the feed impedance matrix and the weighted adjacency matrix of physical prior conditions; The objective function is obtained by multiplying the physical consistency multi-objective residual function by Lagrange multipliers and directional directed acyclic constraints, and then multiplying the result by penalty parameters and directional directed acyclic constraints. The initial directed acyclic graph causal weight matrix that simultaneously satisfies physical consistency, material supply physical laws and acyclic topology is obtained by minimizing the objective function. Based on the initial causal weight matrix and feasible material supply instruction matrix of the directed acyclic graph, the set of causal relationships between nodes is extracted.

[0011] Optionally, constructing the Bayesian posterior physical constraint rule set includes: Construct a set of Bayesian posterior physical constraint rules to constrain causal edge relationships that exist in the initial directed acyclic graph causal weight matrix but do not conform to the physical feeding law of low alloy steel castings; Based on the set of Bayesian posterior physical constraint rules, a Bayesian rule penalty function is constructed to introduce rule control during the NOTEARS optimization process; Based on the physical consistency multi-objective residual function, a Bayesian rule penalty function is introduced to construct an objective function that integrates Bayesian posterior rules. By introducing the directional weighted acyclic constraint function as a constraint term into the objective function of the fused Bayesian posterior rule, a joint optimization objective function is constructed. By performing continuous gradient optimization on the joint optimization objective function, the causal weight matrix of the optimized directed acyclic graph is obtained. Based on the optimized causal weight matrix and material supply feasibility matrix of the directed acyclic graph, the set of causal relationships between nodes is re-filtered and updated.

[0012] Optionally, the set of Bayesian posterior physical constraint rules includes: Gravity direction constraint: If the vertical height of a skeleton node is lower than the vertical height of another skeleton node, then directed causal edges from the skeleton node with higher vertical height to the skeleton node with lower vertical height are prohibited. Riser direction constraint: If a skeleton node is identified as a riser node, the corresponding skeleton node shall not be used as a causal result node of other skeleton nodes. For material supply path constraints, if the material supply feasibility between skeleton nodes is less than the material supply feasibility threshold, then the causal edge between the corresponding skeleton nodes is defined as an edge that cannot be physically realized.

[0013] Optionally, the step of calculating the causal chain risk score by combining the optimized directed acyclic graph causal weight matrix includes: Based on the optimized causal weight matrix of the directed acyclic graph and the updated set of causal relationships between skeleton nodes, a causal path graph structure is constructed. In the causal path graph structure, a breadth-first search algorithm is used to generate all reachable paths by recursively traversing along directed edges, starting from each riser skeleton node. The endpoint of the path is the end skeleton node of the causal chain, and the set of all paths obtained by recursive traversal is the causal chain set. For each causal chain in the causal chain set, extract the end skeleton node of the causal chain and calculate the hot spot risk score of the end skeleton node of the causal chain; For each causal chain endpoint skeleton node in the causal chain set, calculate the hot spot risk score. If the hot spot risk score of a certain causal chain endpoint skeleton node is greater than or equal to the hot spot risk score threshold, then the corresponding skeleton node is included in the hot spot candidate skeleton node set.

[0014] Optionally, mapping the set of candidate skeleton nodes for hot spots back to the 3D digital model of the low-alloy steel casting via skeleton indexing includes: For each skeleton node in the candidate skeleton node set of hot spots, according to the correspondence between the skeleton node index number and the central axis transformation skeleton node set, locate it back to the spatial region in the three-dimensional digital model of the low alloy steel casting to obtain the spatial location data of the hot spot.

[0015] Output the spatial location data of hot spots and display the corresponding spatial location of hot spots in a visual manner in the three-dimensional digital model of low alloy steel castings, so as to realize the prediction of the location of hot spots in low alloy steel castings.

[0016] Optionally, the hot spot spatial location data includes: Three-dimensional spatial coordinates: These are the three-dimensional spatial coordinates of the skeleton nodes in the three-dimensional digital model of the low-alloy steel casting, used to locate the specific positions of the candidate skeleton nodes for hot spots in the casting model; Control volume: The total volume of molten metal corresponding to the control area of ​​the skeleton node, used to measure the amount of feeding required by the skeleton node; Skeleton path distance: The topological path length from the skeleton node to the nearest riser, used to measure the connectivity distance between the skeleton node and the patching source; Local Module: A cooling capacity index for the control area of ​​a skeleton node, used to represent the heat dissipation rate of the skeleton node; Hot spot risk score: This score is calculated jointly based on the optimized causal weights of the directed acyclic graph and the physical load factor of the skeleton node, and is used to reflect the risk level of the skeleton node becoming a hot spot. The physical load factor is the product of the control volume and the local modulus.

[0017] Risk level label: A label that classifies risk levels based on hotspot risk scores and preset thresholds; Upstream causal path chain: This refers to the effective material supply path from the riser skeleton node to the hot spot candidate skeleton node, used to trace the continuity and path dependency of the feeding channel; Cumulative channel impedance: The sum of the shrinkage resistance between all skeleton nodes in the upstream causal path chain, used to measure the overall physical resistance level of the shrinkage path; Number of causal edges before pruning: This is the total number of incoming edges to the skeleton node before the introduction of Bayesian physics rules, used to measure the complexity of the initial causal structure. Number of causal edges after pruning: This is the number of incoming edges that are ultimately retained in the skeleton node after optimization by Bayesian physics rules, reflecting the constraint effect of physics rules on the causal structure.

[0018] The beneficial effects of this invention are: (1) This invention reduces the complexity of the three-dimensional casting model into a lightweight skeleton network by hierarchical central axis transformation, extracts the bifurcation points, endpoints and geometric mutation points as nodes, and constructs the physical feature vector of each node based on the three-dimensional Voronoi space partition. With the skeleton nodes as the reasoning basis of the causal network, the topology of the compensation path between nodes, the flow direction and the regional volume requirements are introduced into the model input to realize the global quantitative modeling of complex compensation links, so that the system can accurately trace the physical causes of hot spots, and the identification of the corresponding hot spot risk areas is more targeted and operable.

[0019] (2) This invention applies NOTEARS’s continuous optimization mapping method to predict the hot spot location of low alloy steel castings, and introduces multi-objective residual loss of the physical features of skeleton nodes, weighted acyclic constraint of feeding direction and feeding impedance penalty. Combined with Bayesian posterior physical rules, the optimization objective function is constructed. During the structure learning process, physically unreasonable causal edges are dynamically eliminated. This not only ensures the consistency of the directed acyclic structure and direction of the causal graph, but also realizes the physical feasibility verification of the feeding path between nodes. The hot spot prediction results are highly consistent with the actual casting defect generation mechanism. In multiple complex process scenarios, it significantly reduces misjudgment and omission, and improves the accuracy and engineering applicability of intelligent recognition.

[0020] (3) This invention constructs a full-process causal chain of pruning from riser to hot node, calculates risk score for each hot node candidate, and outputs three-dimensional hot node spatial location, risk classification and structural traceability evidence by combining the changes in causal structure before and after pruning according to Bayesian physical rules. It can highlight high-risk pruning termination points, visualize path bottlenecks and structural weaknesses with one click. Attached Figure Description

[0021] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 The flowchart shows a method for predicting the location of hot spots in low-alloy steel castings based on Bayesian dynamic inference graphs, as proposed in this invention. Figure 2 This is a schematic diagram of the NOTEARS continuous optimization and Bayesian posterior physical constraint embedding joint optimization process in the method for predicting the hot spot location of low alloy steel castings based on Bayesian dynamic inference graph proposed in this invention. Detailed Implementation

[0022] Example 1: Reference Figures 1-2 A method for predicting the location of hot spots in low-alloy steel castings based on Bayesian dynamic inference graphs, comprising: A three-dimensional digital model of a low-alloy steel casting is acquired and a layered central axis transformation is performed to obtain central axis transformation skeleton data. Based on the central axis transformation skeleton data, bifurcation points, endpoints and geometric gradient abrupt change points are extracted to form a set of central axis transformation skeleton nodes. In this embodiment, bifurcation points, endpoints, and geometric gradient abrupt change points are extracted based on the central axis transformation skeleton data, including: A 3D scanning device was used to acquire the surface and internal geometry of the target low-alloy steel casting to obtain a 3D digital model of the low-alloy steel casting. The three-dimensional digital model data of low alloy steel castings is a three-dimensional mesh model that can represent the geometry of low alloy steel solids. The three-dimensional mesh model adopts a spatial voxel representation method and has clear volume boundary topological and geometric properties.

[0023] A skeleton extraction process based on layered central axis transformation was performed on the three-dimensional digital model of low alloy steel castings to obtain central axis transformation skeleton data; Example 1 specifically includes: calculating the shortest distance from each spatial voxel element in the 3D digital model of the low-alloy steel casting to the surface of the 3D digital model of the low-alloy steel casting to obtain a voxel distance field; selecting a local maximum point in the voxel distance field as the initial central axis point, which is the voxel point farthest from the surface of the 3D digital model of the low-alloy steel casting; performing hierarchical clustering on all initial central axis points, grouping spatially close initial central axis points into the same skeleton branch, tracing the trajectory of the central axis point along each skeleton branch, connecting adjacent central axis points to generate a skeleton path, and integrating all skeleton paths to obtain central axis transformation skeleton data; the central axis transformation skeleton data consists of a set of skeleton points, each skeleton point has a unique 3D spatial coordinate, each set of 3D spatial coordinates consists of x-coordinate, y-coordinate, and z-coordinate, and the total number of skeleton points is the total number of skeleton points.

[0024] Spatial structure analysis is performed on the central axis transformation skeleton data to calculate the connection relationship between each skeleton point. Based on the connection relationship between each skeleton point, a skeleton connection graph structure is constructed, and the central axis transformation skeleton topology network is formed by the skeleton connection graph structure. In Example 1, the spatial structure analysis involves sequentially traversing each skeleton point, identifying all skeleton points directly adjacent to each skeleton point through spatial distance and three-dimensional topological adjacency relationships, establishing a connecting edge for each pair of skeleton points with a direct spatial connection relationship, and collecting all the connecting edges between all skeleton points and their adjacent skeleton points to obtain a combination of the skeleton point set and the set of connecting edges between skeleton points, thus constructing a skeleton connection graph structure. The skeleton connection graph structure uses the skeleton point set as nodes and each pair of directly connected skeleton points as edges. Through the pairing relationship between nodes and edges, it fully expresses the spatial connectivity of the three-dimensional geometric skeleton of the low alloy steel casting, forming a central axis transformation skeleton topological network from the skeleton connection graph structure.

[0025] Based on the central axis transformation skeleton topology network, the set of bifurcation point nodes, the set of endpoint nodes, and the set of geometric gradient abrupt change points are identified; In Example 1, the set of branch point nodes is obtained by traversing each skeleton point in the central axis transformation skeleton topology network. If a skeleton point has three or more directly connected edges, the corresponding skeleton point is divided into branch point nodes, and all skeleton points that meet this condition are gathered together to form a set of branch point nodes.

[0026] The endpoint node set is obtained by traversing each skeleton point in the central axis transformation skeleton topology network. If a skeleton point has only one directly connected edge, then the corresponding skeleton point is divided into endpoint nodes, and all skeleton points that satisfy this condition are gathered together to form the endpoint node set.

[0027] The geometric gradient mutation point set is obtained by calculating the skeleton curvature value for each skeleton point in the central axis transformation skeleton topology network and calculating the average value of the skeleton curvature values ​​of all skeleton points. Iterate through each skeleton point in the central axis transformation skeleton topology network. If the difference between the skeleton curvature value of a skeleton point and the average value of the skeleton curvature is greater than the gradient mutation threshold, then the corresponding skeleton point is divided into a geometric gradient mutation point. All skeleton points that meet this condition are gathered together to form a geometric gradient mutation point set.

[0028] The set of bifurcation point nodes, the set of endpoint nodes, and the set of geometric gradient mutation points are merged and deduplicated to form the set of central axis transformation skeleton nodes.

[0029] Each skeleton node in the central axis transformation skeleton node set represents the initial node of a potential hot spot candidate region in a low alloy steel casting.

[0030] For each skeleton node in the set of central axis transformation skeleton nodes, calculate the local modulus, skeleton path distance to the nearest riser, and control volume, construct the corresponding physical feature vector, and combine all physical feature vectors to generate a candidate node physical feature matrix; In this embodiment, a corresponding physical feature vector is constructed for the set of central axis transformation skeleton nodes, including: For each skeleton node in the set of skeleton nodes for the central axis transformation, obtain the three-dimensional spatial coordinates of the corresponding skeleton node, and calculate the local modulus of the skeleton node based on the three-dimensional spatial coordinates of the skeleton node. The local modulus is a structural parameter representing the heat dissipation capacity of the area controlled by the skeleton node. It is calculated by the ratio of the volume of the area controlled by the skeleton node to the surface area of ​​the area controlled by the skeleton node. The local modulus is used to quantify the cooling capacity of the area corresponding to the skeleton node in low alloy steel castings.

[0031] For each skeleton node in the set of central axis transformation skeleton nodes, perform skeleton path search in the central axis transformation skeleton topology network to obtain the skeleton path distance from the skeleton node to the nearest riser; The skeleton path distance is the sum of the spatial lengths of all skeleton connecting edges on the path from the skeleton node to the nearest riser. The skeleton path distance represents the feeding path length between the skeleton node and the riser in a low alloy steel casting.

[0032] For each skeleton node in the central axis transformation skeleton node set, a region allocation method based on three-dimensional Voronoi space partitioning is adopted to divide the three-dimensional digital model of the low alloy steel casting into multiple node regions, and the control volume of the node region of each skeleton node is calculated. In Example 1, for each skeleton node in the set of central axis transformation skeleton nodes, a region allocation method based on three-dimensional Voronoi spatial partitioning is used to allocate all spatial voxel units in the three-dimensional digital model of the low alloy steel casting to the nearest skeleton node according to the three-dimensional spatial distance of each spatial voxel unit to all skeleton nodes, forming the node region of the skeleton node. For the node region of each skeleton node, the control volume is calculated. The control volume is the sum of the volumes of all spatial voxel units in the node region, that is, the volumes of all spatial voxel units allocated to the skeleton node are accumulated to obtain the control volume of the skeleton node. The control volume is used to quantify the total amount of molten metal controlled by the skeleton node in the low alloy steel casting.

[0033] Based on the local modulus, skeleton path distance, and control volume, the three types of physical parameters of each skeleton node are combined to construct a physical feature vector. The physical feature vectors of all skeleton nodes are combined in the order of node index to generate a candidate node physical feature matrix.

[0034] The physical feature vector is an ordered triple consisting of local modulus, skeleton path distance, and control volume; the candidate node physical feature matrix is ​​a multi-row cell data table composed of the physical feature vectors of all skeleton nodes arranged in order.

[0035] An initial topological skeleton graph structure is established based on the set of nodes of the central axis transformation skeleton and their connectivity relationships; In this embodiment, establishing the initial topological skeleton graph structure includes: For each skeleton node in the set of skeleton nodes in the central axis transformation, each skeleton node in the set of skeleton nodes in the central axis transformation is treated as a graph node, and any pair of skeleton nodes with a direct connected edge relationship is treated as a graph edge, thus constructing the node set and edge set of the initial topological skeleton graph structure. The initial topological skeleton diagram fully expresses the spatial connectivity of the three-dimensional geometric skeleton of the low-alloy steel casting.

[0036] Assign a unique node index number to each skeleton node in the initial topology skeleton graph structure to form an initial topology skeleton graph structure identified by the node index number; Establish a one-to-one correspondence between each node index number and the corresponding skeleton node in the central axis transformation skeleton node set. Based on the node index number, re-encode the node set and edge set in the initial topological skeleton graph structure to form an initial topological skeleton graph structure identified by the node index number.

[0037] The adjacency representation of the initial topological skeleton graph structure is constructed based on the node index number; Each graph edge with two skeleton nodes as endpoints is converted into an adjacency record consisting of the two node index numbers. All adjacency records are summarized to generate an adjacency relationship data table. When necessary, an adjacency relationship matrix is ​​further generated with the node index numbers as row and column indices. The adjacency relationship matrix is ​​a Boolean array indicating whether the skeleton nodes are directly connected. It is used to uniformly represent the topological connection relationship between all skeleton nodes in the initial topological skeleton graph structure.

[0038] Each row of physical feature vectors in the candidate node physical feature matrix is ​​associated with the corresponding skeleton node in the initial topology skeleton graph structure according to the node index number, forming an initial topology skeleton graph structure with physical feature annotations.

[0039] The local modulus, skeleton path distance, and control volume recorded in the physical feature matrix of the candidate node are respectively bound to the corresponding skeleton nodes in the initial topology skeleton graph structure.

[0040] An improved NOTEARS continuous optimization method is adopted, which takes the initial topological skeleton graph structure as input, generates an initial directed acyclic graph causal weight matrix, and extracts the set of causal relationships between nodes. In this embodiment, the improved NOTEARS continuous optimization method includes: The NOTEARS optimization variable is set as a directed weighted adjacency matrix. The directed weighted adjacency matrix is ​​masked according to the adjacency relation matrix of the initial topology skeleton graph structure to obtain the masked directed weighted adjacency matrix. Each element of the directed weighted adjacency matrix corresponds to the weight of the directed causal relationship between the skeleton nodes.

[0041] The mask-constrained directed weighted adjacency matrix retains only skeleton node pairs with directly connected edges, and sets all other elements to zero. In addition, all diagonal elements of the directed weighted adjacency matrix are set to zero.

[0042] Combining the feeding channel characteristics of low alloy steel castings, a feasible feeding instruction matrix is ​​constructed based on the physical feature matrix of candidate nodes. Then, based on the feasible feeding instruction matrix, the mask constraint directed weighted adjacency matrix is ​​weighted at the element level to obtain the physical prior precondition weighted adjacency matrix. In Example 1, each element of the feasible feeding instruction matrix represents the feeding feasibility from one skeleton node to another. The feeding feasibility is obtained by normalizing the local modulus of the target skeleton node minus the local modulus of the source skeleton node, normalizing the skeleton path distance of the target skeleton node minus the skeleton path distance of the source skeleton node, and normalizing the control volume of the target skeleton node minus the control volume of the source skeleton node. After weighting, the results are input into the Logistic function to obtain a feeding feasibility between 0 and 1. The higher the feeding feasibility, the more the feeding path in that direction conforms to the feeding physical logic from thin to thick, from near to far, and from small volume to large volume.

[0043] Construct a feed impedance matrix, where each element measures the difficulty of feeding in a certain direction. A higher feed impedance indicates that it is more difficult to achieve feeding in the corresponding direction.

[0044] ; in, skeleton nodes To skeleton nodes The normalized feed resistance along the feeding path represents the resistance from the node within the low-alloy steel casting. Material supply to nodes The physical resistance strength, the higher the normalized feed resistance, the more obstructed the feeding of molten metal, the node The more likely it is to become a hot spot risk point due to obstructed shrinkage, Represents skeleton nodes The local modulus represents the low-alloy steel casting at the node. The natural cooling capacity of the controlled area Represents skeleton nodes The local modulus, If , then Otherwise, it is 0, indicating that effective causal transmission can only occur if the modulus of the downstream node is greater than that of the upstream node. This represents the mean of the local moduli of all skeleton nodes. Represents skeleton nodes The skeleton path distance to the nearest riser reflects the actual flow length of the feeding path inside the low-alloy steel casting. Represents skeleton nodes Distance of the skeleton path to the nearest riser If , then Otherwise, it is 0, used to express that only downstream nodes far from the riser can become the causal endpoint of the upstream node's shrinking flow. This represents the average distance of the skeleton path from all skeleton nodes to the nearest riser. Represents skeleton nodes The control volume represents the node. The total volume of molten metal required to replenish the controlled area. This represents the average volume of all skeleton nodes.

[0045] Construct a directional weighting matrix, use the directional weighting matrix to weight the physical prior precondition weighted adjacency matrix, and define the directional weighting acyclic constraint to obtain the directional directed acyclic constraint; Each element of the direction-weighted matrix is ​​the normalized positive part of the skeleton path distance of the target skeleton node minus the skeleton path distance of the source skeleton node. The acyclic constraint of the direction-weighted matrix is ​​used to characterize the physical law that the shrinking order is irreversible. The matrix exponent trace operation is used to determine whether the physical prior precondition weighted adjacency matrix satisfies the acyclic structure and the shrinking direction is from near to far.

[0046] ; in, This represents a directional directed acyclic constraint function used to weight the adjacency matrix of physical prior conditions. Introducing the acyclic constraint of physical directionality, The trace operator represents a matrix. Representation matrix Exponentiation, i.e. matrix Power of 1 This represents the direction-weighted matrix, and ○ represents the Hadamard product. This represents the total number of skeleton nodes, which is equal to the number of nodes in the skeleton node set in the low alloy steel casting.

[0047] A physical consistency multi-objective residual function is defined by the feed impedance matrix and the weighted adjacency matrix of physical prior conditions; The physical consistency multi-objective residual function is the square of the L2 norm of the product of the normalized local modulus column vector and the transpose of the physical prior precondition weighted adjacency matrix, the square of the L2 norm of the product of the normalized skeleton path distance column vector and the transpose of the physical prior precondition weighted adjacency matrix, the square of the L2 norm of the product of the normalized control volume column vector and the transpose of the physical prior precondition weighted adjacency matrix, the sum of these three, plus the Frobenius inner product of the absolute values ​​of the elements of the feed impedance matrix and the physical prior precondition weighted adjacency matrix multiplied by the feed impedance penalty coefficient, plus the L1 norm of the absolute values ​​of the elements of the physical prior precondition weighted adjacency matrix multiplied by the sparsity regularization coefficient.

[0048] ; in, This represents the physical consistency multi-objective residual function, used as a measure of the NOTEARS optimization objective in predicting the location of hot spots in low-alloy steel castings. Let be the local modulus eigenvector of all skeleton nodes, representing the cooling capacity of the control region of the skeleton node in the low-alloy steel casting. Let be the skeleton path distance feature vector for all skeleton nodes, representing the length of the shrunk path from the skeleton node to the nearest riser. This represents the control volume feature vector of all skeleton nodes, reflecting the total volume of liquid metal controlled by the skeleton nodes. The square of the Euclidean norm of a vector. Represents the physical prior penalty coefficient. Represents the feed impedance matrix. This represents the inner product of the feed impedance matrix and the weighted adjacency matrix of physical prior conditions, which applies a weighted penalty to edges that violate physical process constraints. This represents the sparsity regularization coefficient.

[0049] By setting a physical consistency multi-objective residual function, not only is the multi-dimensional synergistic effect of the physical characteristics of candidate nodes (local modulus, skeleton path distance, control volume) in predicting hot spot locations comprehensively considered, but the matching between the causal structure constraints of the model and the physical laws of the casting process can also be dynamically taken into account. Specifically, the physical consistency multi-objective residual function can jointly optimize multiple objectives such as the fitting error of the initial directed acyclic graph causal weight matrix output by the model, physical prior bias, and structural acyclicity. This enables the algorithm to achieve efficient causal structure learning while maximally conforming to the actual hot spot formation mechanism of low alloy steel castings. In this way, the problem of the result deviating from the physical reality under single objective optimization is avoided, and the accuracy of hot spot prediction and process interpretability are improved.

[0050] The objective function is obtained by multiplying the physical consistency multi-objective residual function by Lagrange multipliers and directional directed acyclic constraints, and then multiplying the result by penalty parameters and directional directed acyclic constraints. The initial directed acyclic graph causal weight matrix that simultaneously satisfies physical consistency, material supply physical laws and acyclic topology is obtained by minimizing the objective function. Based on the initial causal weight matrix and feasible material supply instruction matrix of the directed acyclic graph, the set of causal relationships between nodes is extracted.

[0051] In Example 1, the directed causal weight in the initial directed acyclic graph causal weight matrix and the material supply feasibility in the feasible material supply indication matrix are read for each skeleton node pair. The directed causal weight is compared with a preset weight threshold. If the directed causal weight is greater than or equal to the weight threshold, the corresponding material supply feasibility is compared with the feasibility threshold. If the material supply feasibility is greater than or equal to the feasibility threshold, the corresponding skeleton node pair is determined as a valid directed causal relationship and identified as a directed causal edge from the source skeleton node to the target skeleton node. All skeleton node pairs that satisfy the condition that the directed causal weight is greater than or equal to the weight threshold and the material supply feasibility is greater than or equal to the feasibility threshold are collected and a set of causal relationships between nodes is formed according to the skeleton node index pairs. Each pair of skeleton nodes in the set of causal relationships between nodes has directionality, representing a valid directed causal connection from the source skeleton node to the target skeleton node in the hot spot prediction of low alloy steel castings.

[0052] Construct a set of Bayesian posterior physical constraint rules, embed the set of Bayesian posterior physical constraint rules as a penalty term into the NOTEARS optimization objective, and perform constraint optimization on the initial directed acyclic graph causal weight matrix and the set of causal relationships between nodes to obtain the optimized directed acyclic graph causal weight matrix and the updated set of causal relationships between nodes. In this embodiment, a set of Bayesian posterior physical constraint rules is constructed, including: Construct a set of Bayesian posterior physical constraint rules to constrain causal edge relationships that exist in the initial directed acyclic graph causal weight matrix but do not conform to the physical feeding law of low alloy steel castings; The set of Bayesian posterior physical constraint rules includes: Gravity direction constraint: If the vertical height of a skeleton node is lower than the vertical height of another skeleton node, then directed causal edges from the skeleton node with higher vertical height to the skeleton node with lower vertical height are prohibited. Riser direction constraint: If a skeleton node is identified as a riser node, the corresponding skeleton node shall not be used as a causal result node of other skeleton nodes. For material supply path constraints, if the material supply feasibility between skeleton nodes is less than the material supply feasibility threshold, then the causal edge between the corresponding skeleton nodes is defined as an edge that cannot be physically realized.

[0053] Based on the set of Bayesian posterior physical constraint rules, a Bayesian rule penalty function is constructed to introduce rule control in the NOTEARS optimization process. For skeleton node pairs that violate gravity direction constraint, riser direction constraint, and material supply path constraint, if there is a causal edge with a directed causal weight greater than zero in the initial directed acyclic graph causal weight matrix for each type of constraint, the corresponding causal edge is penalized. Based on the physical consistency multi-objective residual function, a Bayesian rule penalty function is introduced to construct an objective function that integrates Bayesian posterior rules. The objective function is the sum of the physical consistency multi-objective residual function and the Bayesian rule penalty coefficient multiplied by the Bayesian rule penalty function. The Bayesian rule penalty coefficient is used to balance physical consistency and the strength of physical prior rules.

[0054] By introducing the directional weighted acyclic constraint function as a constraint term into the objective function of the fused Bayesian posterior rule, a joint optimization objective function is constructed. The directional weighted acyclic constraint function is multiplied by the directional acyclic constraint penalty coefficient and added to the objective function that incorporates Bayesian posterior rules to construct a joint optimization objective function. This joint optimization objective function is used to simultaneously constrain the directional acyclic structure, directional physical laws, and Bayesian prior physical rules during the optimization process, ensuring that the optimization process satisfies physical consistency and structural rationality while achieving acyclic topology requirements and directional consistency requirements.

[0055] By performing continuous gradient optimization on the joint optimization objective function, the causal weight matrix of the optimized directed acyclic graph is obtained. In Example 1, for the joint optimization objective function, an iterative solution method based on continuous gradient optimization is adopted. The initial directed acyclic graph causal weight matrix is ​​used as the initial value of the optimization variable. The gradient of the joint optimization objective function with respect to the directed acyclic graph causal weight matrix is ​​calculated. The directed acyclic graph causal weight matrix is ​​updated according to the gradient direction. In each iteration, physical consistency constraints, Bayesian rule penalty terms, and direction-weighted acyclic structure constraints are introduced simultaneously to perform multi-objective joint optimization of the directed acyclic graph causal weight matrix. The iteration continues until the joint optimization objective function converges or reaches the preset optimal condition, and the optimized directed acyclic graph causal weight matrix is ​​obtained. The optimized directed acyclic graph causal weight matrix takes into account structural sparsity, physical feature consistency, directional acyclicity, and Bayesian prior physical rule constraints.

[0056] Based on the optimized causal weight matrix and material supply feasibility matrix of the directed acyclic graph, the set of causal relationships between nodes is re-filtered and updated.

[0057] The logic for re-filtering and updating the set of causal relationships between nodes includes: If the directed causal weight of a pair of skeleton nodes in the optimized directed acyclic graph causal weight matrix is ​​greater than or equal to the directed causal edge weight threshold, and the corresponding material supply feasibility is greater than or equal to the material supply feasibility threshold, then the pair of skeleton nodes is included in the set of causal relationships between nodes. Each pair of skeleton nodes in the set of causal relationships between nodes represents a causal path that is directional and physically feasible.

[0058] The material supply feasibility matrix is ​​a directed relation matrix between skeleton node pairs, used to measure whether it is physically feasible to supply material from one skeleton node to another. Its value ranges from 0 to 1.

[0059] A causal chain is generated based on the updated set of causal relationships between nodes. The risk score of the causal chain is calculated by combining it with the optimized causal weight matrix of the directed acyclic graph, and a set of candidate skeleton nodes for hotspots is formed. In this embodiment, the risk score of the causal chain is calculated by combining the optimized causal weight matrix of the directed acyclic graph, including: Based on the optimized causal weight matrix of the directed acyclic graph and the updated set of causal relationships between skeleton nodes, a causal path graph structure is constructed. The causal path graph structure uses the skeleton node index as the skeleton node set and the updated set of causal relationships between skeleton nodes as the directed edge set, representing the directional channels of feeding causal relationships within low alloy steel castings.

[0060] In the causal path graph structure, a breadth-first search algorithm is used to generate all reachable paths by recursively traversing along directed edges, starting from each riser skeleton node. The endpoint of the path is the end skeleton node of the causal chain, and the set of all paths obtained by recursive traversal is the causal chain set. In Example 1, in the causal path graph structure, a breadth-first search algorithm is used. Starting from each riser skeleton node, all adjacent skeleton nodes are traversed sequentially along the directed edges. For each traversal, when the traversed skeleton node has no outgoing edges or all its outgoing edges point to traversed skeleton nodes, the current path is recorded as a complete path. The starting point of the path is the riser skeleton node, and the ending point is the skeleton node with no subsequent outgoing edges or all its outgoing edges point to traversed skeleton nodes. The above traversal and path recording operation is repeated for all riser skeleton nodes. Each path that meets the above conditions is regarded as a causal chain. All causal chains are gathered to form a causal chain set. Each causal chain in the causal chain set is formed by sequentially connecting the starting point of the path, several consecutive feeding channel skeleton nodes, and the ending point of the path (the end skeleton node of the causal chain), representing all possible feeding paths inside the low alloy steel casting from the riser skeleton node along the feeding channel to the feeding termination skeleton node.

[0061] For each causal chain in the causal chain set, extract the end skeleton node of the causal chain and calculate the hot spot risk score of the end skeleton node of the causal chain; In Example 1, for the end skeleton node of the causal chain, all upstream skeleton nodes pointing to the end skeleton node are traversed. The optimized causal weight of the directed acyclic graph pointing to the end skeleton node of the causal chain is obtained for each upstream skeleton node. Each optimized causal weight of the directed acyclic graph is multiplied by the inverse of its corresponding material supply feasibility. The result is multiplied by the physical load factor of the end skeleton node of the causal chain. The physical load factor is equal to the product of the control volume and the local modulus of the end skeleton node of the causal chain. The above multiplication results of all upstream skeleton nodes to the end skeleton node of the causal chain are accumulated to obtain the hot spot risk score of the end skeleton node of the causal chain. The hot spot risk score is used to measure the possibility that the end skeleton node of the causal chain becomes a high-risk area of ​​feeding obstruction. The physical load factor is used to reflect the potential feeding pressure of the skeleton node. The inverse of the material supply feasibility is used to reflect that the lower the physical feasibility of the feeding channel, the greater the risk of the end skeleton node of the causal chain.

[0062] For each causal chain endpoint skeleton node in the causal chain set, calculate the hot spot risk score. If the hot spot risk score of a certain causal chain endpoint skeleton node is greater than or equal to the hot spot risk score threshold, then the corresponding skeleton node is included in the hot spot candidate skeleton node set.

[0063] The set of candidate skeleton nodes for hot spots is mapped back to the 3D digital model of the low-alloy steel casting through the skeleton index, and the corresponding spatial location data of hot spots is obtained. The corresponding spatial location of hot spots is then displayed in the 3D digital model of the low-alloy steel casting, thus realizing the prediction of hot spot location of low-alloy steel casting.

[0064] In this embodiment, the set of candidate skeleton nodes for hot spots is mapped back to the three-dimensional digital model of the low-alloy steel casting through skeleton indexing, including: For each skeleton node in the candidate skeleton node set of hot spots, according to the correspondence between the skeleton node index number and the central axis transformation skeleton node set, locate it back to the spatial region in the three-dimensional digital model of the low alloy steel casting to obtain the spatial location data of the hot spot.

[0065] Spatial location data of hot spots, including: Three-dimensional spatial coordinates: These are the three-dimensional spatial coordinates of the skeleton nodes in the three-dimensional digital model of the low-alloy steel casting, used to locate the specific positions of the candidate skeleton nodes for hot spots in the casting model; Control volume: The total volume of molten metal corresponding to the control area of ​​the skeleton node, used to measure the amount of feeding required by the skeleton node; Skeleton path distance: The topological path length from the skeleton node to the nearest riser, used to measure the connectivity distance between the skeleton node and the patching source; Local Module: A cooling capacity index for the control area of ​​a skeleton node, used to represent the heat dissipation rate of the skeleton node; Hot spot risk score: This score is calculated jointly based on the optimized causal weights of the directed acyclic graph and the physical load factor of the skeleton node, and is used to reflect the risk level of the skeleton node becoming a hot spot. The physical load factor is the product of the control volume and the local modulus.

[0066] Risk level label: A label that classifies risk levels based on hotspot risk scores and preset thresholds; Upstream causal path chain: This refers to the effective material supply path from the riser skeleton node to the hot spot candidate skeleton node, used to trace the continuity and path dependency of the feeding channel; Cumulative channel impedance: The sum of the shrinkage resistance between all skeleton nodes in the upstream causal path chain, used to measure the overall physical resistance level of the shrinkage path; Number of causal edges before pruning: This is the total number of incoming edges to the skeleton node before the introduction of Bayesian physics rules, used to measure the complexity of the initial causal structure. Number of causal edges after pruning: This is the number of incoming edges that are ultimately retained in the skeleton node after optimization by Bayesian physics rules, reflecting the constraint effect of physics rules on the causal structure.

[0067] Output the spatial location data of hot spots and display the corresponding spatial location of hot spots in a visual manner in the three-dimensional digital model of low alloy steel castings, so as to realize the prediction of the location of hot spots in low alloy steel castings.

[0068] In Example 1, the spatial location data of hot spots is displayed in a visual manner in the three-dimensional digital model of the low-alloy steel casting, and the output grading criteria are as follows: High-risk hotspot areas are defined as hotspot risk scores greater than or equal to a preset high-risk threshold, and cumulative channel impedance greater than or equal to the average cumulative channel impedance of all skeleton nodes. High-risk hotspot areas are marked in red. Medium-risk hotspot areas are those with a risk score in the middle range, and are marked in orange. Low-risk hotspot areas are those with a hotspot risk score below the preset low-risk threshold, and are marked in yellow.

[0069] In the 3D visualization results, each candidate skeleton node of the hot spot is highlighted with a spherical marker in the 3D digital model of the low alloy steel casting. At the same time, the visualization interface displays the node number, 3D spatial coordinates, control volume, skeleton path distance, local module, hot spot risk score, risk level label, upstream causal path chain, cumulative channel impedance, number of causal edges before pruning, and number of causal edges after pruning. This helps casting process engineers to comprehensively analyze the cause path of hot spots, feeding resistance level, and structural change evidence, providing physically interpretable decision-making basis for the design and defect control optimization of low alloy steel castings.

[0070] Example 2: In a low-alloy steel casting production process, the system implemented an intelligent prediction process for the location of hot spots on a low-alloy steel casting with a complex structure, multiple thick junctions and internal cavities.

[0071] The engineer obtained a 3D digital model of the low-alloy steel casting using a 3D scanning device. The 3D digital model of the low-alloy steel casting has a mesh resolution of 1.0 mm and a total number of approximately 21 million elements. The central axis transformation skeleton extraction module performed skeleton discretization on the model, extracting a total of 265 skeleton nodes, including 68 bifurcation points, 45 endpoints, and 83 geometric gradient abrupt change points. The others are ordinary skeleton nodes. Taking skeleton node N41 as an example, its spatial coordinates are (134.2, 280.9, 1465.7). The control area was initially determined to be a thick-walled intersection.

[0072] For each node in the skeleton node set, the system sequentially calculates the local module, skeleton path distance, and control volume. Example 2 uses node N41 as an example; its control volume is 28,100 cm³, its local module is 2.9 cm, and its skeleton path distance is 224 mm. Node N119 (thin-walled stiffener terminal) has a control volume of 7,400 cm³, a local module of 1.1 cm, and a skeleton path distance of 82 mm. The average control volume of all skeleton nodes is 12,870 cm³, the average local module is 2.0 cm, and the average skeleton path distance is 132 mm.

[0073] Based on the skeleton node set, the system established an initial topological skeleton graph structure with 265 nodes and 420 directly connected edges. The nodes were automatically numbered and an adjacency matrix was generated. In Example 2, nodes N41 and N87 are used as examples. There are directly connected edges between them, and the corresponding element in the adjacency matrix is ​​1.

[0074] All node physical feature vectors are written into the candidate node physical feature matrix in sequence. The 17th row is [2.3,165, 10,950] and the 122nd row is [3.6, 215, 35,800]. All feature data are normalized and then used for subsequent modeling.

[0075] During the NOTEARS continuous optimization phase, the optimization variable is a 265×265 directed weighted adjacency matrix. After the initial mask constraint, all non-connected elements and diagonal elements are set to zero. Combined with the physical feature system, a feasible feed indication matrix and a feed impedance matrix are constructed. The feed feasibility is 0.93 and the feed impedance is 0.14 when N41 points to N87; the feed feasibility is 0.18 and the impedance is 0.82 when N119 points to N41. A set of Bayesian physical constraint rules is introduced, prohibiting nodes such as N240 (identified as a riser node) from being the causal endpoint of other nodes; if the height z of N87 is lower than that of N41, N41 cannot point to N87.

[0076] After joint optimization, the number of incoming edges in the causal weight matrix of the directed acyclic graph was reduced from 6 to 2, all of which are feasible channels in the direction of shaving. All incoming edges of node N221 were pruned because the material supply feasibility was less than 0.3, and N221 became an isolated node. Before pruning, the average weight of incoming edges of N41 was 0.45, and after pruning it was 0.31.

[0077] Based on the updated set of causal relationships between nodes, the system starts from each riser node and uses a breadth-first search to generate all shrinkage chains. A certain shrinkage chain starts from riser node N240, and the path passes through N138, N162, and terminates at N41. N41, as the terminal node of the causal chain, has its hot spot risk score calculated as follows: its upstream nodes are N138 and N162, with optimization weights of 0.37 and 0.34 respectively pointing to N41, corresponding to material supply feasibility of 0.78 and 0.67. The physical load factor of N41 is 28100 × 2.9 = 81490, and the hot spot risk score is: 0.37×(1-0.78)×81490 + 0.34×(1-0.67)×81490 = 0.37×0.22×81490 + 0.34×0.33×81490 ≈ 6,637 + 9132 ≈ 15769.

[0078] All chain end nodes were ranked by risk score. The top 10% of nodes had a hot node risk score greater than 15,000 and a cumulative channel impedance greater than 1.05. Nodes N41 and N197 were identified as high-risk hot node candidates, while node N87, with a risk score of 11,040, was identified as a medium-risk node.

[0079] The system backmaps candidate skeleton nodes for high, medium, and low-risk hot spots to the 3D digital model of the casting according to the mapping relationship between node index numbers and skeleton sets. The spatial coordinates of N41 are (134.2, 280.9, 1465.7), and those of N197 are (285.5, 389.2, 1492.8). The output hot spot spatial location data includes node number, 3D coordinates, control volume, path distance, local modulus, risk score, risk level, upstream chain, and cumulative channel impedance. In the visualization interface, N41 is highlighted in red, indicating "high risk"; N87 is highlighted in orange, indicating "medium risk"; and the remaining low-risk nodes are highlighted in yellow.

[0080] Compared to traditional finite element thermal simulation, which takes 156 minutes to predict the location of hot spots in the casting, requiring manual interpretation by engineers and failing to explain specific feeding paths and bottlenecks, this invention completes the entire process of intelligent prediction and hierarchical output in just 11 minutes. The average positioning error of high-risk hot spot areas predicted by the traditional method is 39.2 mm, while the average positioning error of this invention is 13.9 mm. In this batch of 5 castings, the traditional method missed 3 hot spots, requiring 2 manual corrections. Using this invention, all 5 castings correctly identified hot spots. After the process engineer added risers and chills at the system-suggested locations, shrinkage defects no longer occurred. All X-ray inspections showed no defects at high-risk hot spots, increasing the yield by 9.3%. Specific training and verification sample data are shown in Table 1 (partial). Table 1 Training and Validation Sample Data

[0081] The data from this invention are compared with those from traditional finite element thermal simulation, and the comparison data is shown in Table 2 below: Table 2. Data comparison between the present invention and traditional finite element thermal simulation.

[0082] Example 2 shows that the method of the present invention can achieve full-link automation, interpretable intelligent reasoning and process optimization suggestions in the prediction of hot spots in complex low alloy steel castings.

[0083] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting the location of hot spots in low-alloy steel castings based on Bayesian dynamic inference graphs, characterized in that, include: A three-dimensional digital model of a low-alloy steel casting is acquired and a layered central axis transformation is performed to obtain central axis transformation skeleton data. Based on the central axis transformation skeleton data, bifurcation points, endpoints and geometric gradient abrupt change points are extracted to form a set of central axis transformation skeleton nodes. For the set of skeleton nodes of the central axis transformation, construct the corresponding physical feature vectors, and combine all physical feature vectors to generate the physical feature matrix of candidate nodes; An initial topological skeleton graph structure is established based on the set of nodes of the central axis transformation skeleton and their connectivity relationships; An improved NOTEARS continuous optimization method is adopted, which takes the initial topological skeleton graph structure as input, generates an initial directed acyclic graph causal weight matrix, and extracts the set of causal relationships between nodes. Construct a set of Bayesian posterior physical constraint rules, embed the set of Bayesian posterior physical constraint rules as a penalty term into the NOTEARS optimization objective, and perform constraint optimization on the initial directed acyclic graph causal weight matrix and the set of causal relationships between nodes to obtain the optimized directed acyclic graph causal weight matrix and the updated set of causal relationships between nodes. A causal chain is generated based on the updated set of causal relationships between nodes. The risk score of the causal chain is calculated by combining the optimized causal weight matrix of the directed acyclic graph, and a set of candidate skeleton nodes for hotspot nodes is formed. The candidate skeleton node set of hot spots is mapped back to the three-dimensional digital model of the low alloy steel casting to obtain the spatial location data of the hot spots. The corresponding spatial location of the hot spots is then displayed in the three-dimensional digital model of the low alloy steel casting, thus completing the prediction of the hot spot location of the low alloy steel casting.

2. The method for predicting the location of hot spots in low-alloy steel castings based on Bayesian dynamic inference graphs according to claim 1, characterized in that, The extraction of bifurcation points, endpoints, and geometric gradient abrupt change points based on the central axis transformation skeleton data includes: A 3D scanning device was used to acquire the surface and internal geometry of the target low-alloy steel casting to obtain a 3D digital model of the low-alloy steel casting. The three-dimensional digital model of the low alloy steel casting is subjected to skeleton extraction processing based on layered central axis transformation to obtain central axis transformation skeleton data; Spatial structure analysis is performed on the central axis transformation skeleton data to calculate the connection relationship between each skeleton point. Based on the connection relationship between each skeleton point, a skeleton connection graph structure is constructed, and a central axis transformation skeleton topology network is formed from the skeleton connection graph structure. Based on the central axis transformation skeleton topology network, the set of bifurcation point nodes, the set of endpoint nodes, and the set of geometric gradient abrupt change points are identified; The set of bifurcation point nodes, the set of endpoint nodes, and the set of geometric gradient mutation points are merged and deduplicated to form the set of central axis transformation skeleton nodes.

3. The method for predicting the location of hot spots in low-alloy steel castings based on Bayesian dynamic inference graphs according to claim 1, characterized in that, The construction of the corresponding physical feature vector for the set of central axis transformation skeleton nodes includes: For each skeleton node in the set of skeleton nodes for the central axis transformation, obtain the three-dimensional spatial coordinates of the corresponding skeleton node, and calculate the local modulus of the skeleton node based on the three-dimensional spatial coordinates of the skeleton node. For each skeleton node in the set of central axis transformation skeleton nodes, perform skeleton path search in the central axis transformation skeleton topology network to obtain the skeleton path distance from the skeleton node to the nearest riser; For each skeleton node in the central axis transformation skeleton node set, a region allocation method based on three-dimensional Voronoi space partitioning is adopted to divide the three-dimensional digital model of the low alloy steel casting into multiple node regions, and the control volume of the node region of each skeleton node is calculated. Based on the local modulus, skeleton path distance, and control volume, the three types of physical parameters of each skeleton node are combined to construct a physical feature vector. The physical feature vectors of all skeleton nodes are combined in the order of node index to generate a candidate node physical feature matrix.

4. The method for predicting the location of hot spots in low-alloy steel castings based on Bayesian dynamic inference graphs according to claim 1, characterized in that, The establishment of the initial topological skeleton graph structure includes: For each skeleton node in the set of skeleton nodes in the central axis transformation, each skeleton node in the set of skeleton nodes in the central axis transformation is treated as a graph node, and any pair of skeleton nodes with a direct connected edge relationship is treated as a graph edge, thus constructing the node set and edge set of the initial topological skeleton graph structure. Assign a unique node index number to each skeleton node in the initial topology skeleton graph structure to form an initial topology skeleton graph structure identified by the node index number; The adjacency relationship representation of the initial topological skeleton graph structure is constructed based on the node index number; Each row of physical feature vectors in the candidate node physical feature matrix is ​​associated with the corresponding skeleton node in the initial topology skeleton graph structure according to the node index number, forming an initial topology skeleton graph structure with physical feature annotations.

5. The method for predicting the location of hot spots in low-alloy steel castings based on Bayesian dynamic inference graphs according to claim 1, characterized in that, The improved NOTEARS continuous optimization method includes: The NOTEARS optimization variable is set as a directed weighted adjacency matrix. The directed weighted adjacency matrix is ​​masked according to the adjacency relation matrix of the initial topology skeleton graph structure to obtain the masked directed weighted adjacency matrix. Combining the feeding channel characteristics of low alloy steel castings, a feasible feeding instruction matrix is ​​constructed based on the physical feature matrix of candidate nodes. Then, based on the feasible feeding instruction matrix, the mask constraint directed weighted adjacency matrix is ​​weighted at the element level to obtain the physical prior precondition weighted adjacency matrix. Construct a feed impedance matrix, where each element measures the feeding difficulty in a certain direction. Construct a directional weighting matrix, use the directional weighting matrix to weight the physical prior precondition weighted adjacency matrix, and define the directional weighting acyclic constraint to obtain the directional directed acyclic constraint; A physical consistency multi-objective residual function is defined by the feed impedance matrix and the weighted adjacency matrix of physical prior conditions; The objective function is obtained by multiplying the physical consistency multi-objective residual function by Lagrange multipliers and directional directed acyclic constraints, and then multiplying the result by penalty parameters and directional directed acyclic constraints. The initial directed acyclic graph causal weight matrix that simultaneously satisfies physical consistency, material supply physical laws and acyclic topology is obtained by minimizing the objective function. Based on the initial causal weight matrix and feasible material supply instruction matrix of the directed acyclic graph, the set of causal relationships between nodes is extracted.

6. The method for predicting the location of hot spots in low-alloy steel castings based on Bayesian dynamic inference graphs according to claim 1, characterized in that, The construction of the Bayesian posterior physical constraint rule set includes: Construct a set of Bayesian posterior physical constraint rules to constrain causal edge relationships that exist in the initial directed acyclic graph causal weight matrix but do not conform to the physical feeding law of low alloy steel castings; Based on the set of Bayesian posterior physical constraint rules, a Bayesian rule penalty function is constructed to introduce rule control during the NOTEARS optimization process; Based on the physical consistency multi-objective residual function, a Bayesian rule penalty function is introduced to construct an objective function that integrates Bayesian posterior rules. By introducing the directional weighted acyclic constraint function as a constraint term into the objective function of the fused Bayesian posterior rule, a joint optimization objective function is constructed. By performing continuous gradient optimization on the joint optimization objective function, the causal weight matrix of the optimized directed acyclic graph is obtained. Based on the optimized causal weight matrix and material supply feasibility matrix of the directed acyclic graph, the set of causal relationships between nodes is re-filtered and updated.

7. The method for predicting the location of hot spots in low-alloy steel castings based on Bayesian dynamic inference graphs according to claim 6, characterized in that, The set of Bayesian posterior physical constraint rules includes: Gravity direction constraint: If the vertical height of a skeleton node is lower than the vertical height of another skeleton node, then directed causal edges from the skeleton node with higher vertical height to the skeleton node with lower vertical height are prohibited. Riser direction constraint: If a skeleton node is identified as a riser node, the corresponding skeleton node shall not be used as a causal result node of other skeleton nodes. For material supply path constraints, if the material supply feasibility between skeleton nodes is less than the material supply feasibility threshold, then the causal edge between the corresponding skeleton nodes is defined as an edge that cannot be physically realized.

8. The method for predicting the location of hot spots in low-alloy steel castings based on Bayesian dynamic inference graphs according to claim 1, characterized in that, The calculation of the causal chain risk score by combining the optimized directed acyclic graph causal weight matrix includes: Based on the optimized causal weight matrix of the directed acyclic graph and the updated set of causal relationships between skeleton nodes, a causal path graph structure is constructed. In the causal path graph structure, a breadth-first search algorithm is used to generate all reachable paths by recursively traversing along directed edges, starting from each riser skeleton node. The endpoint of the path is the end skeleton node of the causal chain, and the set of all paths obtained by recursive traversal is the causal chain set. For each causal chain in the causal chain set, extract the end skeleton node of the causal chain and calculate the hot spot risk score of the end skeleton node of the causal chain; For each causal chain endpoint skeleton node in the causal chain set, calculate the hot spot risk score. If the hot spot risk score of a certain causal chain endpoint skeleton node is greater than or equal to the hot spot risk score threshold, then the corresponding skeleton node is included in the hot spot candidate skeleton node set.

9. The method for predicting the location of hot spots in low-alloy steel castings based on Bayesian dynamic inference graphs according to claim 1, characterized in that, The process of mapping the set of candidate skeleton nodes for hot spots back to the 3D digital model of the low-alloy steel casting via skeleton indexing includes: For each skeleton node in the candidate skeleton node set of hot spots, according to the correspondence between the skeleton node index number and the central axis transformation skeleton node set, locate it back to the spatial region in the three-dimensional digital model of the low alloy steel casting to obtain the spatial location data of the hot spot.

10. The method for predicting the location of hot spots in low-alloy steel castings based on Bayesian dynamic inference graphs according to claim 9, characterized in that, The hot spot spatial location data includes: Three-dimensional spatial coordinates: These are the three-dimensional spatial coordinates of the skeleton nodes in the three-dimensional digital model of the low-alloy steel casting, used to locate the specific positions of the candidate skeleton nodes for hot spots in the casting model. Control volume: The total volume of molten metal corresponding to the control area of ​​the skeleton node, used to measure the amount of feeding required by the skeleton node; Skeleton path distance: The topological path length from the skeleton node to the nearest riser, used to measure the connectivity distance between the skeleton node and the patching source; Local Module: A cooling capacity index for the control area of ​​a skeleton node, used to represent the heat dissipation rate of the skeleton node; Hot spot risk score: This score is calculated jointly based on the optimized causal weights of the directed acyclic graph and the physical load factor of the skeleton node, and is used to reflect the risk level of the skeleton node becoming a hot spot. Risk level label: A label that classifies risk levels based on hotspot risk scores and preset thresholds; Upstream causal path chain: the effective material supply path from the riser skeleton node to the hot spot candidate skeleton node, used to trace the continuity and path dependency of the feeding channel; Cumulative channel impedance: The sum of the shrinkage resistance between all skeleton nodes in the upstream causal path chain, used to measure the overall physical resistance level of the shrinkage path; Number of causal edges before pruning: This is the total number of incoming edges to the skeleton node before the introduction of Bayesian physics rules, used to measure the complexity of the initial causal structure. Number of causal edges after pruning: This is the number of incoming edges that are ultimately retained in the skeleton node after optimization by Bayesian physics rules, reflecting the constraint effect of physics rules on the causal structure.

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