A method for optimizing casting parameters of a low-temperature medium centrifugal pump impeller

Abstract

The present application relates to computer-aided casting and low-temperature equipment manufacturing data processing technical field, specifically to a kind of low-temperature medium centrifugal pump impeller casting parameter optimization method, the time sequence field data of impeller filling, solidification, cooling, heat treatment and low-temperature cooling stage is obtained, cross-stage grid correspondence is established, and temperature, liquid phase rate, solidification shrinkage, insufficient feeding and residual stress state are transferred according to energy, defect quantity and stress state conservation;According to the low-temperature medium temperature zone, construct low-temperature risk field, trace back the defect formation area and formation period, convert the tracking results into pouring temperature, filling speed, cooling boundary strength and the optimization weight of holding time sequence, directional disturbance is carried out to associated parameters, and the parameter combination satisfying filling, feeding, residual stress and low-temperature risk constraint is screened out.The present application makes low-temperature risk correspond to the casting formation process, reduces the deviation between normal temperature evaluation and low-temperature service requirement.

Description

Technical Field

[0001] This invention relates to the field of computer-aided casting and cryogenic equipment manufacturing data processing technology, specifically a method for optimizing casting parameters of a cryogenic medium centrifugal pump impeller. Background Technology

[0002] Impellers of cryogenic centrifugal pumps are typically manufactured using precision casting or sand casting processes. Their casting quality is directly influenced by parameters such as pouring temperature, filling rate, initial mold temperature, cooling boundary strength, and holding time. Existing technologies generally begin by establishing a three-dimensional casting model of the impeller, dividing the impeller cavity into a finite computational mesh, and then performing numerical calculations based on molten metal flow, heat transfer, solidification shrinkage, and feeding conditions. During the calculation process, filling integrity, solidification time, liquid phase ratio change, shrinkage cavity volume, and residual stress are used as the main evaluation indicators. Casting parameters are adjusted through experimental design, response surface methodology, genetic search, or surrogate models. Conventional optimization typically aims to minimize shrinkage cavity volume, shorten solidification time, or reduce residual stress, selecting a combination of parameters from multiple candidate combinations that meets the casting quality requirements, and then correcting the model parameters based on trial production results. This approach can reflect the temperature field and solidification state of the impeller hub, blade root, and flow channel transition region during the casting stage, but the evaluation process mainly focuses on quality indicators after demolding or at room temperature.

[0003] Some existing technologies further divide the filling, solidification, demolding cooling, and heat treatment into continuous calculation stages. After the previous stage is completed, the temperature, phase state, or stress results are used as the initial conditions for the next stage to analyze the state changes of the impeller in different manufacturing stages. For impellers of cryogenic centrifugal pumps, a cryogenic cooling model can also be established separately after the casting calculation is completed. The cryogenic shrinkage deformation and local stress distribution are calculated based on the material's thermal expansion coefficient, temperature change range, and boundary constraints. Such schemes usually use grid interpolation to transfer data between different stages and determine whether the casting defect index and cryogenic performance index meet the preset conditions. When stress concentration or deformation exceeding the limit occurs in the cryogenic calculation, the pouring temperature, cooling rate, or heat treatment parameters are usually readjusted, and the casting and cryogenic calculations are repeated. Because the grid scale, calculation variables, and evaluation objectives are different in each stage, conventional data transfer often only retains the average temperature or overall stress. Insufficient local feeding, compositional segregation, and defect peaks are easily weakened during stage transitions, and cryogenic risks are difficult to correspond to specific defect formation areas and formation periods.

[0004] The lack of a reverse-trackable state correlation between casting parameter optimization and low-temperature service performance evaluation means that parameter adjustments are still based on room-temperature casting quality indicators. Insufficient feeding, compositional segregation, and non-uniform residual stress formed during impeller solidification continue to propagate and recombine during subsequent cooling, heat treatment, and low-temperature cooling processes, ultimately leading to low-temperature shrinkage mismatch, localized stress amplification, or defect propagation. Even when existing methods perform cascade calculations across multiple manufacturing stages, they typically only observe state changes in the forward direction, failing to determine the corresponding solidification region, formation period, and related casting parameters from the low-temperature risk area. Therefore, it is impossible to determine which casting state variables caused a particular risk and when it formed. The resulting optimal parameter combination may reduce room-temperature shrinkage porosity, but it still retains defect sources amplified under low-temperature conditions, making the parameter optimization results inconsistent with the actual low-temperature service requirements of the impeller and hindering the formation of a closed-loop parameter optimization basis oriented towards low-temperature service conditions. Summary of the Invention

[0005] The purpose of this invention is to provide a method for optimizing the casting parameters of a cryogenic medium centrifugal pump impeller, which can solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for optimizing casting parameters of a cryogenic centrifugal pump impeller includes: acquiring time-series field data of the impeller during the filling, solidification, demolding and cooling, heat treatment and cryogenic service cooling stages, and establishing cross-stage grid correspondence based on a unified spatial identifier; Based on the conservation of energy, defect, and stress state, the temperature history, liquidus ratio change, solidification shrinkage, degree of insufficient feeding, compositional segregation characterization value, and residual stress state of the previous stage are projected to the next stage. Based on the low-temperature medium temperature range and cooling process, the low-temperature shrinkage mismatch value, local stress amplification value and defect propagation driving value are calculated to form a low-temperature risk field. Based on the low-temperature risk field, the defect formation area and formation time are traced in reverse, and the tracing results are converted into optimized weights for pouring temperature, filling speed, initial mold temperature, cooling boundary strength, and heat preservation sequence. The casting parameters associated with the formation period are subjected to directional perturbation according to the optimization weights, and parameter combinations that satisfy the filling constraints, solidification feeding constraints, residual stress constraints and low temperature risk constraints are selected.

[0007] Preferably, the establishment of the cross-stage grid correspondence includes: generating a spatial index for each stage computational grid, consisting of impeller reference coordinates, material region identifiers, and local topology numbers; For regions where the grid scales are inconsistent in adjacent stages, the volume overlap coefficient between the source grid cell and the target grid cell is calculated, and a state transfer matrix is ​​constructed using the volume overlap coefficient. Integral conservation projection was used for temperature history and liquid fraction change, while peak preservation projection was used for the degree of insufficient feeding, compositional segregation characterization value and residual stress state. When the same target grid cell corresponds to multiple source grid cells, the projection priority is determined based on the solidification time proximity and material phase consistency, and the spatial source index and stage source index of each projection state are recorded.

[0008] Preferably, the reverse tracking includes: constructing a mesh element risk vector according to the low-temperature shrinkage mismatch value, the local stress amplification value, and the defect propagation driving value; The stage back mapping weights are extracted from the mesh correspondence between adjacent stages and the projection coefficients used for state projection, and the first back contribution matrix is ​​obtained based on the stage back mapping weights between the low-temperature service cooling stage and the heat treatment stage. The first inverse contribution matrix is ​​propagated in reverse by sequentially using the stage inverse mapping weights between the heat treatment stage, demolding and cooling stage, solidification stage and filling stage; At each stage, the reverse propagation results are screened based on the location of the liquid phase rate change, the connectivity of the feeding channel, and the main direction of residual stress. This forms a reverse contribution path pointing from the low-temperature risk grid cell to the defect formation area, formation time period, and corresponding state variables. The contribution amount is then assigned to each reverse contribution path.

[0009] Preferably, the directional disturbance includes: establishing a parameter actionable matrix based on the temporal overlap relationship between each casting parameter in the reverse contribution path and the defect formation period, and excluding parameters that do not have an actionable range outside the defect formation period; The contribution of the reverse contribution path is allocated to the pouring temperature, filling speed, initial mold temperature, cooling boundary strength and heat preservation time according to the parameter action matrix to generate time-segmented optimization weights; Based on the time-segmented optimization weights, the perturbation direction and perturbation order of each parameter are determined, and candidate parameter combinations are generated using the local proxy model constructed from the completed casting calculation samples. Perform cross-stage computation chain verification on the candidate parameter combinations, and update the effective sample domain of the local proxy model based on the verification results.

[0010] Preferably, the construction of the state transfer matrix further includes: setting the impeller hub, blade root, flow channel transition region and blade body region as independent transfer subdomains, and forming an initial matrix in each transfer subdomain according to the volume overlap relationship between the source grid cell and the target grid cell; Calculate the total enthalpy difference, solidification shrinkage difference, and residual stress tensor invariant difference before and after the initial matrix projection, and decompose each difference to the corresponding target mesh element; The projection coefficients of the target grid cell are iteratively corrected using the spatial source index as a constraint until each transfer subdomain satisfies the preset conserved residual range; For the target mesh element located at the boundary of the transfer subdomain, the cross-domain correction coefficient is configured based on the heat flow direction of the adjacent region and the solidification front normal vector.

[0011] Preferably, the formation of the reverse contribution path further includes: taking the low-temperature risk grid cell as the endpoint, setting the moment when the liquid phase fraction changes from a continuous distribution to an isolated distribution during the solidification stage as a candidate formation node, and setting the moment when the cross-sectional area of ​​the feeding channel decreases as a candidate transfer node. A set of directed paths is constructed based on the spatial connectivity between the candidate forming nodes, the candidate transmission nodes and the low-temperature risk grid cells; Calculate the direct contribution of component segregation characterization value, solidification shrinkage and residual stress state to the risk vector in each directed path, as well as the indirect contribution transmitted through intermediate nodes. Directed paths whose direct and indirect contributions cancel each other out and whose combined contribution is below the path retention condition are removed, and the retained paths are sorted according to their formation time sequence.

[0012] Preferably, the construction of the local proxy model includes: using casting parameters with non-zero weights optimized in different time periods as input variables, and using the degree of insufficient feeding, residual stress state, and low temperature risk vector in the defect formation area as joint output variables; A local sample neighborhood is constructed based on the distance between the candidate parameter combination and the completed casting calculation sample, and weights are assigned to the neighborhood samples based on the consistency of the formation time of the reverse contribution path. Within the local sample neighborhood, a piecewise response surface is established between the input variable and the joint output variable. Segments whose response change direction is inconsistent with the contribution direction of the reverse contribution path are marked as mismatch segments. When generating the candidate parameter combination, the candidate points are restricted to be located within a continuous trusted domain composed of non-mismatched segments.

[0013] Preferably, the cross-stage calculation chain verification includes: substituting the candidate parameter combination into the filling stage and solidification stage calculations, and extracting the newly generated solidification front connectivity state, feeding channel state and isolated liquid phase region distribution; When the newly generated state changes the node connection relationship of the reverse contribution path, the reverse contribution path and the time-segmented optimization weights are recalculated, and the corresponding candidate parameter combination is returned to the local proxy model for further perturbation. When the node connection relationship remains unchanged, continue to perform the calculation of the demolding cooling, heat treatment and low temperature service cooling stages, and compare the consistency of the projection state of each stage with the joint output variable corresponding to the candidate parameter combination. Only candidate parameter combinations whose state deviations at each stage are all within the effective sample domain of the local proxy model are retained.

[0014] Preferably, it further includes: after completing the cross-stage calculation of the candidate parameter combination, pairing the newly calculated grid state with the corresponding projection state according to the spatial source index to form a propagation error sample; Based on the clustering location of the transmission error samples in each transmission subdomain, the transmission error volume overlap coefficient, the peak preservation projection error, and the cross-domain correction coefficient, the low-temperature risk field is regenerated using the corrected state transmission matrix and reverse tracking is performed. Compare the set of defect formation areas, the set of formation time periods, and the risk contribution ranking of each formation area before and after the correction; The weights are updated and optimized based on the tracking results where the formation area remains consistent but the risk contribution changes. The tracking results of changes in the formation region are used to redetermine the associated casting parameters, and the updated results are used for the next round of directional perturbation.

[0015] Preferably, it also includes: applying joint perturbations corresponding to the uncertainty interval of the calculation input to the material thermal conductivity, latent heat of solidification, interfacial heat transfer conditions and the cooling rate of the cryogenic medium for the retained candidate parameter combinations; Under each set of joint perturbations, local proxy model prediction and cross-stage calculation chain verification are performed to obtain the set of filling state, solidification and feeding state, residual stress state and low temperature risk field corresponding to the candidate perturbation combination. Calculate the minimum distance between each set of states and the corresponding constraint boundary, and construct the joint feasibility of the candidate parameter combinations based on each minimum distance; Among the candidate parameter combinations where the node connection relationships of the reverse contribution path remain unchanged, the parameter combination with the largest joint feasibility ranking value is selected as the optimization result.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. By establishing a unified spatial correspondence between the stages of filling, solidification, demolding and cooling, heat treatment, and low-temperature service cooling, and by transferring temperature history, liquidus ratio changes, solidification shrinkage, insufficient feeding degree, compositional segregation characterization value, and residual stress state according to the conservation of energy value, defect value, and stress state, local defect peaks and their spatial sources can be retained during stage transitions. Based on this, a low-temperature risk field is formed according to the low-temperature shrinkage mismatch value, local stress amplification value, and defect propagation driving value. Then, using stage reverse mapping weights, the low-temperature risk is propagated backward to the heat treatment, demolding and cooling, solidification, and filling stages to determine the defect formation area, formation time period, and related state variables. This allows the low-temperature service risk to be converted into time-segmented optimization weights for pouring temperature, filling speed, initial mold temperature, cooling boundary strength, and holding time sequence, concentrating parameter disturbances on the corresponding defect formation time window. This avoids indiscriminate adjustments based solely on room-temperature defect indicators, ensuring that the resulting parameter combination is simultaneously constrained by filling, feeding, residual stress, and low-temperature risk.

[0017] 2. To address the issue of inconsistent mesh scales across different stages, a state transfer matrix is ​​constructed based on volume overlap relationships. Integral conservation projection, peak preservation projection, and cross-domain correction are employed to reduce deviations in total enthalpy, solidification shrinkage, and residual stress states caused by mesh transformation. Reverse contribution paths are constructed using spatial source indices, stage source indices, candidate formation nodes, and candidate transfer nodes. Paths where direct and indirect contributions cancel each other out are eliminated, while defect evolution chains with continuous state associations to low-temperature risks are retained. By combining time-segmented optimization weights to establish local sample neighborhoods and piecewise response relationships, candidate parameters are restricted to a continuous confidence domain aligned with the reverse contribution direction. Contribution paths are recalculated when candidate parameters change the solidification front or the connection relationship of the feeding channel. After applying joint perturbations to material thermal conductivity, latent heat of solidification, interfacial heat transfer conditions, and the cooling rate of the low-temperature medium, parameter combinations can be screened based on the minimum distance between each state set and the constraint boundary, reducing the impact of single-calculation errors or input fluctuations on the optimization results. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the overall process of optimizing the casting parameters of a cryogenic centrifugal pump impeller. Figure 2 Flowchart for establishing cross-stage grid correspondence and transferring casting state conservation; Figure 3 A flowchart for constructing a low-temperature risk field, reverse tracing the defect formation process, and generating time-segmented optimized weights; Figure 4 Flowchart for local proxy calculation, candidate parameter generation, cross-stage verification, and joint perturbation screening; Figure 5 A conservation correction graph for cross-stage state transfer; Figure 6 This is a comprehensive risk decomposition diagram of the low-temperature risk field; Figure 7 Contribution map of the reverse contribution path; Figure 8 Optimize the weighting graph of casting parameters across different time periods; Figure 9 For local response surface prediction and confidence domain residual plot; Figure 10 This is a ranking graph of joint perturbation feasibility. Detailed Implementation

[0019] In one embodiment, please refer to Figure 1 This paper provides a method for optimizing casting parameters of a cryogenic centrifugal pump impeller. The method includes acquiring temporal field data of the impeller during the filling, solidification, demolding cooling, heat treatment, and cryogenic service cooling stages, and establishing cross-stage grid correspondences based on a unified spatial identifier. Following the conservation of energy, defect values, and stress state, the method projects the temperature history, liquidus ratio change, solidification shrinkage, degree of insufficient feeding, compositional segregation characterization value, and residual stress state of the previous stage to the next stage. Based on the cryogenic medium temperature range and cooling process, the method calculates the cryogenic shrinkage mismatch value, local stress amplification value, and defect propagation driving value to form a cryogenic risk field. Finally, the method uses the cryogenic risk field to trace the defect formation area in reverse. The tracking results are converted into optimized weights for pouring temperature, filling rate, initial mold temperature, cooling boundary strength, and holding time sequence, based on the domain and formation period. Targeted perturbations are applied to casting parameters associated with the formation period according to these optimized weights. Parameter combinations that satisfy filling constraints, solidification feeding constraints, residual stress constraints, and low-temperature risk constraints are selected. Specifically, the impeller geometry model, casting material thermophysical property data, casting boundary data, and low-temperature medium temperature history are used as inputs. The same impeller reference coordinates are used to describe the calculation results for each stage, and the stage outputs are saved as a time-series field dataset with spatial, temporal, material phase, and state variable indices.

[0020] In this embodiment, the temporal field data of the filling stage includes the molten metal temperature, flow filling state, and free liquid surface arrival time of each grid cell; the temporal field data of the solidification stage includes liquid phase ratio, solidification sequence, cumulative volume shrinkage, feeding channel connectivity, and local component segregation characterization value; the temporal field data of the demolding cooling stage and heat treatment stage includes temperature history, thermal strain history, and residual stress tensor; the temporal field data of the cryogenic service cooling stage includes shrinkage strain, constraint stress, and defect tip driving force driven by the cryogenic medium temperature zone and cooling process; the unified spatial identifier is composed of impeller reference coordinates, material region identifier, local topology number, and stage identifier; the impeller reference coordinates take the rotation axis as the longitudinal reference and the hub reference section as the axial zero point; the material region identifier is used to distinguish the hub, blade root, flow channel transition area, and blade body area; the local topology number is used to identify the adjacency order of grid cells in the same area; and the stage identifier is used to record the source of state variables.

[0021] ; in, This represents the q-th type of state variable of the target mesh element j in the (r+1)-th stage. Represents the source mesh element in stage r. Similar state quantities, This represents the projection coefficient determined by volume overlap, material phase consistency, and solidification time proximity. This represents the number of source mesh cells participating in the projection at stage r. This represents the correction amount applied to satisfy the conservation of energy, defect, or stress state. q takes the corresponding state category among temperature history, liquidus ratio change, solidification shrinkage, degree of insufficient feeding, compositional segregation characterization value, and residual stress state. For example, when the volume overlap ratios of the target mesh element and two source mesh elements are 0.6 and 0.4 respectively, and their material phases are consistent, the temperature history can use 0.6 and 0.4 as the basic projection coefficients. When the second source mesh element contains a local insufficient feeding peak, the defect projection is corrected for the second source mesh element by peak preservation correction and... The difference in total defect quantity is compensated to ensure that the sources of local defects in the target mesh are not lost due to averaging.

[0022] Please refer to Figure 5 , Figure 5 The horizontal axis represents the stage transition and state sequence number, used to unfold cross-stage projection records according to a unified spatial identifier and stage origin order; the vertical axis represents the conservation correction amount, with values ​​varying around the zero baseline. The black curve corresponds to the correction magnitude formed by the conservation constraints of energy, defect, or stress state for each projection record, and the gray dashed line represents the zero baseline. Figure 5 The marked position is the correction point with the largest absolute deviation among all records.

[0023] from Figure 5 As can be seen, the conservation corrections for most of the projected records are close to the zero reference, indicating that the volume overlap coefficient, material phase consistency, and solidification time proximity between adjacent stages can stably inherit the state variables of the source stage without large-scale state variable drift. Local peaks mainly appear near stage transitions and state category transitions, indicating that the degree of insufficient feeding, compositional segregation characterization values, or residual stress states need to be compensated for by conservation corrections in these regions.

[0024] Figure 5 Corresponding to the cross-stage state transfer formula, the distribution of the correction term in different target grid cells is shown. Figure 5 The maximum deviation point marked in the diagram is used to indicate projection records that need to be reviewed. If the point corresponds to the blade root or flow channel transition area, the source grid cell list, projection coefficient list, and stage source list should be further checked to confirm that the source of local defects has not been lost due to grid remapping or averaged projection. The overall trend shows that the proposed cross-stage projection method can achieve state conservation while maintaining spatial correspondence, providing a continuous and traceable initial state for subsequent low-temperature risk field calculations.

[0025] Specifically, the cross-stage state transfer is executed step by step according to the stage time sequence. At the end of the filling, the metal liquid temperature history, filling time, and flow stagnation zone are projected to the initial solidification field. At the end of solidification, the solidification shrinkage, insufficient feeding degree, compositional segregation characterization value, and solidification end temperature field are projected to the initial demolding cooling field. At the end of demolding cooling, the thermal strain history and residual stress state are projected to the initial heat treatment field. At the end of heat treatment, the residual stress state after temperature homogenization, the characterization value of unresolved defects, and the material region state are projected to the initial low-temperature service cooling field. During the projection process, the temperature and liquidus ratio are protected by integral conservation. The insufficient feeding degree and compositional segregation characterization value are protected by a combination of local peak values ​​and total values. The residual stress state is protected by a combination of stress tensor invariants and principal directions. The source mesh cell list, projection coefficient list, and stage source list are saved for each target mesh cell.

[0026] The calculation of the low-temperature risk field uses the state data after heat treatment as the initial condition. The target low-temperature medium temperature zone is discretized into continuous temperature nodes. According to the actual cooling process of the impeller, thermal shrinkage and stress redistribution calculations are performed between adjacent temperature nodes. The low-temperature shrinkage mismatch value is jointly determined by the free shrinkage strain difference of adjacent grid cells, the material region constraint relationship, and the temperature gradient. The local stress amplification value is determined by the change of the maximum principal stress in the low-temperature stage relative to the corresponding principal stress at the end of heat treatment. The defect propagation driving value is jointly determined by the degree of insufficient feeding, the compositional segregation characterization value, the angle relationship between the residual stress principal direction and the low-temperature principal stress direction, and the stress gradient in the defect neighborhood. The calculation results are written back to each grid cell according to a unified spatial identifier and constitute a low-temperature risk field that can be retrieved across stages.

[0027] ; in, This represents the comprehensive risk value of grid cell k during the cooling phase of low-temperature service. This indicates the low-temperature shrinkage mismatch value. Indicates the local stress amplification value. Indicates the defect extension driving value, to This represents the non-negative weights determined based on the material region and the temperature history of the cryogenic medium, where The coupling term used to characterize the shrinkage mismatch and stress amplification. This term is used to characterize the coupling between stress amplification and defect propagation. For example, when the mesh element at the root of a blade... , and When normalized to 0.5, 0.7, and 0.6 respectively, and the five weights are set to 0.2, 0.2, 0.25, and 0.15 respectively, the results are... It includes both individual risks and coupled risks. If only shrinkage mismatch is reduced while stress amplification and defect propagation drivers remain at high values, the risk value will not be masked by the individual decrease, and the true ranking relationship of the low-temperature risk area will be preserved.

[0028] Please refer to Figure 6 , Figure 6 The horizontal axis represents the grid sampling sequence number, corresponding to the risk grid unfolded under a unified spatial identifier during the cryogenic service cooling phase; the vertical axis represents the comprehensive risk value, with a higher value indicating a higher probability of shrinkage mismatch, stress amplification, and defect-driven coupling in that grid cell under the influence of the cryogenic medium. The black curve represents the comprehensive risk distribution of the cryogenic risk field, while the gray dashed line and gray dotted line represent the first and second warning thresholds, respectively. Figure 6 The middle arrow marks the risk peak point in the current sampling sequence.

[0029] from Figure 6As can be seen, the risk curve is generally below the first warning threshold, but shows a significant local rise in several grid segments, indicating that the risk is not uniformly distributed, but rather spatially aggregated according to material regions, temperature nodes, and defect sources. The risk value near the peak point is higher than that of adjacent grids, usually corresponding to the blade root, flow channel transition region, or weakened region of the feeding channel. This indicates that low-temperature shrinkage mismatch and local stress amplification are superimposed at this location, and the defect propagation drive further amplifies the risk ranking.

[0030] Figure 6 Corresponding to the low-temperature risk field formula, each sampling point in the curve is determined by the low-temperature shrinkage mismatch value, the local stress amplification value, the defect propagation driving value, and their coupling terms. Figure 6 The mid-peak value annotation can serve as a direct basis for screening low-temperature risk grid cells, determining the starting point for subsequent reverse tracing. The overall trend indicates that the comprehensive risk calculation not only reflects individual risks but also preserves the coupling effect between shrinkage mismatch and stress amplification, and stress amplification and defect propagation, making the ranking of high-risk areas during the low-temperature service cooling phase more consistent with the actual constrained state of the impeller structure.

[0031] In a preferred embodiment, please refer to Figure 3 The reverse tracing is performed in the following order: low-temperature risk grid cells, heat treatment stage source grid cells, demolding and cooling stage source grid cells, solidification stage source grid cells, and filling stage source grid cells. First, a grid cell risk vector is constructed based on the low-temperature shrinkage mismatch value, local stress amplification value, and defect propagation driving value. Then, the stage reverse mapping weights are extracted from the grid correspondence between adjacent stages and the projection coefficients used for state projection. The first reverse contribution matrix is ​​obtained based on the stage reverse mapping weights between the low-temperature service cooling stage and the heat treatment stage. Subsequently, the first reverse contribution matrix is ​​reverse propagated sequentially using the stage reverse mapping weights between the heat treatment stage, demolding and cooling stage, solidification stage, and filling stage. At each stage, the reverse propagation results are screened based on the liquid phase rate mutation location, the feeding channel connectivity status, and the residual stress principal direction to form a reverse contribution path from the low-temperature risk grid cell to the defect formation area, formation time period, and corresponding state variable. The contribution amount is then configured for each reverse contribution path.

[0032] ; in, Let L represent the contribution of the low-temperature risk grid cell k to the source node u in the s-th stage of backpropagation, and let L represent the stage number of the low-temperature service cooling stage. This indicates the grid nodes traversed by the reverse contribution path in stage h. Indicates the node of stage h Mapped to the next stage node The reverse mapping weights recorded at the time, This represents the path retention coefficient determined based on the abrupt change in liquid fraction, the connectivity of the feeding channel, and the principal direction of residual stress. and This indicates the same source node. For example, when a low-temperature risk grid cell backtracks along three stages and the corresponding reverse mapping weights are 0.8, 0.7, and 0.6 respectively, and the path retention coefficients are 1, 0.9, and 0.8 respectively, the contribution of the source node is obtained by multiplying these weights by the risk value. If an intermediate node does not have a sudden change in liquid rate or has no connection with the feed channel, the corresponding path retention coefficient is 0 and the path is terminated.

[0033] Please refer to Figure 7 , Figure 7 The horizontal axis represents the reverse path sequence, i.e., the candidate paths formed by tracing back from the low-temperature risk grid cell to the heat treatment, demolding cooling, solidification, and filling stages; the vertical axis represents the path contribution, used to characterize the contribution intensity of each source node to the low-temperature risk grid cell. The black curve represents the contribution change of each reverse contribution path, and the gray dashed line represents the average contribution level. Figure 7 The middle arrow indicates the path location with the highest contribution.

[0034] from Figure 7 As can be seen, the contribution of some reverse paths is significantly higher than the average contribution level, indicating that the low-temperature risk is not uniformly formed by all historical states, but is dominated by a few source nodes with high reverse mapping weights and high path retention coefficients. The contribution peaks usually correspond to paths with abrupt changes in liquidus fraction during solidification, a decrease in the connectivity of feeding channels, or a strong continuation of the principal direction of residual stress, indicating that these state variables continue to propagate and amplify the low-temperature risk in subsequent stages.

[0035] Figure 7 Corresponding to the formula for reverse contribution, the path contribution is formed by multiplying the low temperature risk value, the reverse mapping weight of each stage, and the path retention coefficient. Figure 7 Mid-peak value annotations are used to locate the main defect formation sources and propagation paths. Paths with contributions below the average level and mutually canceling directions can be eliminated. The overall trend shows that the reverse tracing method can trace back from high-risk grid cells to the defect formation region, formation period, and key state variables, providing reliable input for subsequent parameter action matrix construction and optimization of perturbation direction selection.

[0036] The reverse contribution path is established using a directed graph data structure with time constraints. Graph nodes record at least a unified spatial identifier, stage identifier, state variable category, state quantity value, and time index. Graph edges record state projection relationships, spatial adjacency relationships, heat flow transfer relationships, and shrinkage path relationships. Low-temperature risk grid cells serve as endpoint nodes. The moment when the liquid fraction changes from a continuous distribution to an isolated distribution during the solidification stage is set as a candidate forming node. The moment when the cross-sectional area of ​​the shrinkage channel decreases is set as a candidate transfer node. A set of directed paths is constructed based on the spatial connectivity between candidate forming nodes, candidate transfer nodes, and low-temperature risk grid cells. The direct contribution of component segregation characterization value, solidification shrinkage, and residual stress state to the risk vector and the indirect contribution transmitted through intermediate nodes are calculated for each directed path. Directed paths where the direct and indirect contribution directions cancel each other out and the combined contribution is lower than the path retention condition are eliminated. The retained paths are sorted according to the order of their formation time.

[0037] In this embodiment, the direct contribution is obtained by fixing other state variables in the same path and changing the input value of the target state variable. The indirect contribution is obtained by fixing the target state variable and retaining its transmission relationship to intermediate nodes. For example, for the risk of low-temperature stress amplification at the root of the blade, the solidification shrinkage is kept at the actual value and the composition segregation characterization value is replaced with the reference value of the same region. The difference between the low-temperature risk vector and the original risk vector is recalculated as the direct contribution of the composition segregation characterization value. Then, the composition segregation characterization value is kept at the actual value but its transmission edge to the residual stress state in the heat treatment stage is blocked. The resulting risk difference is used as the indirect contribution transmitted through the residual stress state. When the direct contribution and the indirect contribution are in the same direction, the corresponding directed path is retained. When the directions are opposite, it is determined whether to retain it according to the synthetic contribution amount, so that the reverse tracing result can distinguish the formation source of the defect state and the subsequent amplification source.

[0038] Furthermore, a parameter action matrix is ​​established based on the temporal overlap between each casting parameter in the reverse contribution path and the defect formation period. The pouring temperature is associated with the entire filling process and the initial solidification stage; the filling speed is associated with the arrival time of the molten metal, the free liquid surface advancement process, and the early heat input; the initial mold temperature is associated with the filling heat transfer and the initial solidification temperature difference; the cooling boundary strength is associated with the solidification front movement and temperature gradient within its application period; and the holding time sequence is associated with the temperature equalization of the later solidification stage, the demolding cooling stage, and the heat treatment stage. The parameter action matrix sets the parameter elements that do not cover the defect formation period to 0, and sets the parameter elements that cover the defect formation period and have data correlation with the state variables of the reverse contribution path to non-zero values, thereby excluding parameters that do not have an action range outside the defect formation period.

[0039] ; in, This represents the time-division optimization weight of the casting parameter m within the time window t. This indicates the number of retained reverse contribution paths. This represents the contribution of the p-th reverse contribution path. This represents the time overlap coefficient between the p-th path and parameter m within the time window t. This represents the sensitivity coefficient of parameter m to the direction of the target state variable in the p-th path. This indicates the number of casting parameters involved in the optimization. This indicates the prevention of positive numbers with a denominator of 0. For example, when a defect formation path is mainly located in the later stage of solidification and the time overlap coefficient and direction sensitivity coefficient of the cooling boundary strength with that path are both higher than the filling rate, the cooling boundary strength will achieve a larger value within the corresponding time window. The filling speed does not enter the directional disturbance of this time window because the time overlap coefficient is close to 0.

[0040] Please refer to Figure 8 , Figure 8 The horizontal axis represents the time window, expanded according to the relevant intervals of filling, solidification, heat treatment, and low-temperature service cooling; the vertical axis represents the weight of the time window, used to quantify the adjustable influence of different casting parameters on the reverse contribution path within a specific time window. Different grayscale curves correspond to parameters such as filling speed, initial mold temperature, pouring temperature, holding time sequence, and cooling boundary strength, respectively. The legend indicates the parameter category represented by each curve. Figure 8 The highlighted position indicates the current highest priority.

[0041] from Figure 8 As can be seen, the peak weights of different parameters are not concentrated in the same stage. Filling speed and pouring temperature have a more significant effect in the initial stages of filling and solidification, while the holding time sequence and cooling boundary strength have higher weights within the relevant time windows of heat treatment or low-temperature cooling, indicating that the influence of different parameters on the defect formation path has obvious time interval selectivity. The highest weight indicates that this parameter simultaneously possesses a high path contribution, a high time overlap coefficient, and a strong directional sensitivity within the corresponding time window, and should preferentially enter the directional perturbation sequence.

[0042] Figure 8 Corresponding to the time-segmented optimization weight formula, the curve value is determined by the contribution of the reverse contribution path, the time overlap between the parameters and the path, and the sensitivity of the parameter direction. Figure 8 The separation trends of the curves indicate that the method can exclude parameters that do not have an effective range outside the defect formation period, thus avoiding indiscriminate perturbation of all process parameters. By reading the peak time window and its corresponding parameters, the parameter perturbation order and joint perturbation vector can be formed, providing a clear temporal basis for the subsequent generation of candidate parameter combinations.

[0043] The direction of parameter perturbation is determined based on the direction sensitivity coefficient, which is obtained by applying positive and negative perturbations to a single parameter in the existing sample neighborhood and comparing the change direction of the joint output variable. When the positive perturbation causes the degree of insufficient compensation, residual stress state, and low temperature risk vector to decrease along the contribution direction of the reverse contribution path, the positive direction is set as a candidate perturbation direction. When the negative perturbation meets the same condition, the negative direction is set as a candidate perturbation direction. When both the positive and negative perturbations cause changes in the connection relationship of nodes in the reverse contribution path, the parameter is marked as a topology-sensitive parameter and the single perturbation interval is narrowed. The perturbation order is determined according to the optimization weight of the time period from large to small. When there are multiple parameters in the same time window, a joint perturbation vector is generated based on the state coupling relationship between the parameters instead of using independent continuous modifications.

[0044] In a preferred embodiment, please refer to Figure 2 The establishment of cross-stage grid correspondence includes generating a spatial index for each stage's computational grid, consisting of impeller reference coordinates, material region identifiers, and local topological indices. For regions with inconsistent grid scales in adjacent stages, the volume overlap coefficient between source and target grid cells is calculated, and a state transfer matrix is ​​constructed using the volume overlap coefficient. Integral conservation projection is used for temperature history and liquidus rate changes, and peak preservation projection is used for the degree of insufficient feeding, compositional segregation characterization values, and residual stress state. When the same target grid cell corresponds to multiple source grid cells, the projection priority is determined based on the solidification time proximity and material phase consistency. The spatial source index and stage source index of each projection state are recorded. The spatial index is generated by a combination of coordinate interval coding and topological adjacency coding, so that the same physical region can still be matched through coordinate intervals and adjacency relationships after the grid is re-divided.

[0045] Specifically, the volume overlap coefficient is obtained by dividing the overlap volume of the source grid cell and the target grid cell in a unified reference coordinate system by the volume of the target grid cell. When the target grid cell overlaps with multiple source grid cells, all basic overlap coefficients are normalized to form the initial projection column. When projecting the temperature history, the temperature of the source grid cell, its volume, and the specific heat of the material are all included in the energy integral. When projecting the liquidus rate change, the liquidus volume is treated as a conserved object. When projecting the degree of insufficient feeding and the characterization value of compositional segregation, the volume weighted value and the local maximum value are preserved respectively. When projecting the residual stress state, the first invariant, the second deviatoric stress invariant, and the direction of the maximum principal stress of the stress tensor are preserved. The initial projection column is reordered according to the solidification time difference and the material phase difference between the target grid cell and the source grid cell.

[0046] Preferably, the impeller hub, blade root, flow channel transition region, and blade body region are each set as an independent transfer subdomain. An initial matrix is ​​formed in each transfer subdomain according to the volume overlap relationship between the source grid cell and the target grid cell. The total enthalpy difference, solidification shrinkage difference, and residual stress tensor invariant difference before and after the initial matrix projection are calculated, and each difference is decomposed to the corresponding target grid cell. The projection coefficient of the target grid cell is iteratively corrected with the spatial source index as a constraint until each transfer subdomain meets the preset conserved residual range. For the target grid cell located at the boundary of the transfer subdomain, cross-domain correction coefficients are configured according to the heat flow direction of the adjacent region and the solidification front normal vector. Cross-domain correction is only performed when the spatial adjacency relationship is continuous and the material region boundary allows heat or stress transfer, so as to avoid the defect peak inside the hub being unconditionally diffused to the blade body region.

[0047] The iterative correction within the transfer subdomain employs a constrained residual allocation method. The total enthalpy difference is allocated according to the heat capacity of the target grid cell and its overlap ratio with the source grid cells. The solidification shrinkage difference is allocated according to the correlation between the solidification end time of the target grid cell and the isolated liquid phase region. The residual stress tensor invariant difference is allocated according to the similarity of the principal stress directions and the topological adjacency of the target grid cell. After each round of correction, the corresponding conserved residual is recalculated. When the correction of a target grid cell leads to a local peak value lower than the maximum defect value among all its source grid cells, a peak value lower limit constraint is applied to the target grid cell, and the remaining residual is transferred to adjacent target grid cells within the same transfer subdomain until the conservation condition and the peak value preservation condition are simultaneously satisfied.

[0048] In another preferred embodiment, please refer to Figure 4 The local surrogate model uses casting parameters with non-zero weights optimized in different time periods as input variables, and the degree of insufficient feeding, residual stress state, and low-temperature risk vector within the defect formation region as joint output variables. It constructs a local sample neighborhood based on the distance between the candidate parameter combination and the completed casting calculation samples, and assigns weights to the neighborhood samples based on the consistency of the formation time of the reverse contribution path. Within the local sample neighborhood, a piecewise response surface is established between the input variables and the joint output variables. Segments whose response change direction is inconsistent with the contribution direction of the reverse contribution path are marked as mismatched segments. When generating candidate parameter combinations, the candidate points are restricted to be located within the continuous confidence domain composed of non-mismatched segments. The local sample neighborhood is updated with the position of the current candidate parameter combination, so that the surrogate calculation only uses samples that match the current reverse contribution path and parameter action time window.

[0049] ; in, This represents the joint output prediction value of class b corresponding to the a-th candidate parameter combination. This represents the m-th locally normalized casting parameter in the a-th candidate parameter combination. This represents the local constant term in the output of class b. This represents the local first-order response coefficient of the m-th parameter to the b-th type of output. This represents the local coupling response coefficient between the m-th parameter and the n-th parameter with respect to the b-th type of output. For example, when the pouring temperature and the initial mold temperature are coupled in the same direction to the degree of insufficient feeding at the blade root, the corresponding... Taking a positive value, when the cooling boundary strength and the heat preservation time sequence can form a compensatory relationship within the same formation period, the corresponding... Taking negative values, candidate parameter combinations only enter the continuous confidence domain when the predicted change direction is consistent with the descent direction required by the reverse contribution path.

[0050] Please refer to Figure 9 , Figure 9 The horizontal axis represents candidate parameter combinations, arranged in order of candidate versions; the vertical axis represents the joint output predicted value and the confidence region residual. The black curve represents the joint output predicted value given by the local response surface model, and the gray dashed line represents the confidence region residual of the corresponding candidate point. Figure 9 The middle arrow marks the peak point of the residual. Figure 9 This is used to simultaneously observe the optimized output direction of candidate combinations and the credibility of local proxy models.

[0051] from Figure 9 As can be seen, there are significant differences in the joint output predictions of different candidate parameter combinations, indicating a nonlinear coupling response between parameters such as pouring temperature, initial mold temperature, cooling boundary strength, and holding time. When the residual curve remains at a low level overall, it indicates that the candidate point is located in a continuous confidence domain consistent with the local sample neighborhood and topological label; when the residual shows a peak, it indicates that the candidate point may be close to the segment boundary, or that its solidification front connectivity or feeding channel state differs from that of the neighboring samples, requiring further confirmation through new cross-stage calculation samples.

[0052] Figure 9 Corresponding to the local response surface formula, the predicted value is formed by the local constant term, the first-order response term, and the parameter-coupled response term. Figure 9 The residual peak annotation is used to indicate uncertain regions in the local surrogate model, avoiding cross-segment interpolation of samples with inconsistent topological labels. The overall trend shows that the local surrogate model can quickly filter candidate parameter combinations while maintaining the consistency of the reverse contribution path direction, and prevent unreliable candidate points from entering the final optimization set through the confidence region residual constraint.

[0053] The segmented response surface is established with the condition that the connection relationship of the nodes of the reverse contribution path remains consistent. For each sample in the local sample neighborhood, the solidification front connectivity state, the compensation channel state, and the distribution of the isolated liquid phase region are extracted and encoded as topological labels. Samples with the same topological label are used to fit the same segmented response surface, and samples with different topological labels are not interpolated across segments. The continuous confidence domain consists of regions in the input parameter space with consistent topological labels, prediction residuals that meet the sample error conditions, and joint output change directions that conform to the reverse contribution direction. When a candidate point is close to the segment boundary, cross-stage calculation samples for confirming the topological label are generated first, and the segment boundary position and local response coefficients are updated with the new samples.

[0054] In this embodiment, the generation of candidate parameter combinations starts from the current parameter combination. Multiple joint perturbation vectors are constructed according to the time-segmented optimization weights and parameter perturbation directions. Each joint perturbation vector contains only parameters with non-zero parameters that can act as matrix elements within the same defect formation time window. The parameter changes are restricted to the continuous confidence domain covered by the local sample neighborhood. The predicted values ​​of insufficient feeding, residual stress state, and low-temperature risk vector are calculated using a local surrogate model. Candidate points that violate filling constraints, solidification feeding constraints, residual stress constraints, or low-temperature risk constraints are excluded. The remaining candidate points are then sorted according to the total amount of reverse contribution paths, parameter change norm, and confidence domain boundary distance. Candidate parameter combinations for cross-stage calculation chain verification are selected.

[0055] In a preferred embodiment, the cross-stage calculation chain verification substitutes candidate parameter combinations into the filling stage and solidification stage calculations, extracts the newly generated solidification front connectivity state, feeding channel state, and isolated liquid phase region distribution. When the newly generated state changes the node connection relationship of the reverse contribution path, the reverse contribution path and time-segmented optimization weights are recalculated, and the corresponding candidate parameter combination is returned to the local proxy model for further perturbation. When the node connection relationship remains unchanged, the demolding cooling, heat treatment, and low-temperature service cooling stage calculations are continued. The consistency of the projected state of each stage with the joint output variables corresponding to the candidate parameter combination is compared, and only candidate parameter combinations whose state deviations of each stage are located within the effective sample domain of the local proxy model are retained. The state deviations are calculated in the same material region and the same stage according to a unified spatial identifier.

[0056] When a candidate parameter combination causes a change in the connectivity state of the solidification front but still meets the single defect index, it is not directly identified as a usable combination. Instead, the directed graph nodes and edges are regenerated with new isolated liquid phase regions, feeding channels, and low-temperature risk regions, and the low-temperature risk backpropagation is re-executed. If the new back contribution path points to different defect formation regions or different formation periods, the parameter action matrix and time-segmented optimization weights are re-established. If the new back contribution path still points to the original defect formation region but the contribution ranking changes, the original parameter set is retained and the perturbation order is updated. This allows the candidate parameter search to be adjusted according to the changes in the defect formation mechanism, without covering different solidification topology states with a fixed proxy relationship.

[0057] Furthermore, after completing the cross-stage calculation of the candidate parameter combination, the newly calculated grid state and the corresponding projected state are paired according to the spatial source index to form a transfer error sample. Based on the aggregation position of the transfer error sample in each transfer subdomain, the volume overlap coefficient, peak preservation projection coefficient and cross-domain correction coefficient are corrected respectively. The low-temperature risk field is regenerated using the corrected state transfer matrix and reverse tracking is performed. The defect formation region set, formation time period set and risk contribution ranking corresponding to each formation region are compared before and after correction. The tracking results where the formation region remains consistent but the risk contribution changes are updated and optimized. The tracking results where the formation region changes are re-determined and the associated casting parameters are re-determined. The updated results are used for the next round of directional perturbation.

[0058] The transmitted error samples include temperature history error, liquidus ratio change error, solidification shrinkage error, insufficient feeding error, component segregation characterization error, and residual stress state error. The error samples are clustered according to the transmitted subdomain, stage source, and spatial source. When the errors are concentrated within the same transmitted subdomain, the volume overlap coefficient and peak preservation projection coefficient are corrected first. When the errors are continuously distributed along the boundary of the transmitted subdomain, the cross-domain correction coefficient is corrected first. When the residual stress state error is mainly manifested as a deflection of the main direction, the directional similarity weight in the stress state projection is adjusted. When the solidification shrinkage error and the location of the isolated liquid phase region are offset at the same time, the solidification time proximity weight is adjusted. The corrected coefficients still need to satisfy the conservation conditions of each transmitted subdomain and the source index constraint.

[0059] In another preferred embodiment, joint perturbations corresponding to the uncertainty intervals of the calculation input are applied to the material thermal conductivity, latent heat of solidification, interfacial heat transfer conditions, and cryogenic medium cooling rate for the retained candidate parameter combinations. Under each set of joint perturbations, local surrogate model prediction and cross-stage calculation chain sampling verification are performed to obtain the filling state set, solidification feeding state set, residual stress state set, and cryogenic risk field set corresponding to the candidate parameter combinations. The minimum distance between each state set and the corresponding constraint boundary is calculated, and the joint feasibility of the candidate parameter combinations is constructed based on each minimum distance. Among the candidate parameter combinations in which the node connection relationship of the reverse contribution path remains unchanged, the parameter combination with the largest joint feasibility ranking value is selected as the optimization result. The joint perturbation samples are generated according to the correlation between the changes in thermal properties, the changes in interfacial heat transfer, and the changes in the cryogenic cooling process, rather than using arbitrary combinations that are independent of each other.

[0060] ; in, This represents the joint feasibility of the a-th candidate parameter combination. This represents the set of joint perturbation samples applied to the a-th candidate parameter combination. This represents the distance between the filling state and the filling constraint boundary under the g-th group of joint perturbations. This represents the distance between the solidification and feeding state and the feeding constraint boundary. This represents the distance between the residual stress state and the stress constraint boundary. This represents the distance between the low-temperature risk field and the low-temperature risk constraint boundary. to Represents the normalized weights of the distances to the four types of constraints. This represents the proportion of changes in the connectivity of the reverse contribution path nodes caused by the candidate parameter combination under joint perturbation. This represents the topology change penalty coefficient. For example, when a candidate parameter combination has a large compensation distance in most perturbation samples but the low-temperature risk distance is close to the constraint boundary in a few samples, the minimum operation is controlled by the low-temperature risk distance. The fact that other states have a large margin does not obscure the fact that the low-temperature risk boundary is close.

[0061] Please refer to Figure 10 , Figure 10 The horizontal axis represents candidate parameter combinations, arranged according to the comprehensive ranking results; the vertical axis represents joint feasibility, with higher values ​​indicating greater comprehensive margins in terms of filling stability, feeding connectivity, residual stress limitation, and low-temperature risk control. The black line represents the joint feasibility of each candidate combination, and the gray dashed line represents the lower limit. Figure 10 The middle arrow marks the low-value candidate combination.

[0062] from Figure 10 As can be seen, the top-ranked candidate combinations usually remain above the lower limit, indicating that they have a certain safety margin in multiple constraint dimensions; the bottom-ranked candidate combinations are close to or below the lower limit, indicating that at least one constraint dimension has become a controlling constraint. Low-value combinations may be due to insufficient filling distance, insufficient feeding distance, too small residual stress distance, or insufficient low-temperature risk distance, or they may be penalized due to an excessively high proportion of topological changes, requiring a re-examination of their perturbation amplitude and parameter combination relationships.

[0063] Figure 10 Corresponding to the joint feasibility formula, the joint feasibility is the minimum value among the weighted results of the distances of each constraint, and the topology change penalty term is deducted. Figure 10 Low and medium value labels are used to screen out candidate combinations that are unacceptable or require review, while high value regions can serve as a candidate set for recommended parameter combinations. The overall trend shows that the joint screening method can avoid the situation where improving a single indicator worsens other constraints, ensuring that the final output casting parameter combination simultaneously meets the requirements for filling, feeding, stress, and low-temperature service risk control.

[0064] The generation of joint perturbations is based on the batch correlation between material thermal conductivity and latent heat of solidification, the state correlation between interfacial heat transfer conditions and mold temperature history, and the time correlation between the cooling rate of the low-temperature medium and the boundary heat transfer history. First, the allowable variation range and correlation direction of each uncertain input are determined from existing material data and casting calculation calibration data. Then, stratified sampling is used to generate perturbation combinations covering the boundary and interior of the interval. The prediction results given by the local proxy model are only screened and not directly used as the final feasibility basis. Perturbation combinations that are near the constraint boundary or cause changes in the ranking of the contribution of the reverse contribution path are entered into cross-stage calculation chain sampling verification. After the calculation is completed, the new samples are written into the local sample neighborhood and the continuous confidence domain is updated.

[0065] In a specific application embodiment, the impeller model is divided into transfer subdomains according to the hub, blade root, flow channel transition area, and blade body area. The original casting parameter combination is used to perform filling, solidification, demolding cooling, and heat treatment calculations. The heat treatment end state is transferred to the low-temperature service cooling stage. The low-temperature risk field shows that a certain blade root and the adjacent flow channel transition area form a continuous risk zone. The reverse tracing results show that the risk zone mainly comes from the decrease in the cross-sectional area of ​​the feeding channel after solidification, the formation of local isolated liquid phase areas, and the retention of the main direction of residual stress after heat treatment. The parameter action matrix sets the elements of the filling speed in the corresponding formation period to 0, and sets the staged cooling intensity and heat holding sequence to non-zero elements. The local proxy model generates candidate parameter combinations for the joint change of cooling boundary intensity and heat holding sequence, and judges whether the connection state of the solidification front is consistent through cross-stage calculation chain.

[0066] For the aforementioned specific applications, if a candidate parameter combination causes the isolated liquid phase region to disappear but creates a new feeding channel in the adjacent blade body region that closes prematurely, then a reverse contribution path is re-established and the newly formed region is included in the optimization scope. The parameter weights corresponding to the original risk zone are no longer used. If the candidate parameter combination keeps the defect formation region unchanged and ensures that the degree of insufficient feeding, residual stress state, and low-temperature risk vector are all within the constraint range, then a joint perturbation is applied to the material thermal conductivity, latent heat of solidification, interfacial heat transfer conditions, and low-temperature medium cooling rate. Based on the joint feasibility, combinations that are close to any constraint boundary or frequently cause changes in the path node connection relationship are screened out. The final output includes casting parameter combinations including pouring temperature, filling speed, initial mold temperature, time-segmented cooling boundary strength, and heat preservation sequence, as well as the formation time associated records corresponding to each parameter.

[0067] In one extended application embodiment, when the number of historical casting calculation samples is limited, local perturbation samples are generated centered on the current parameter combination and its reverse contribution path. Priority is given to selecting the parameter direction with a larger time-segment optimization weight to perform cross-stage calculations. The solidification topology label, state transfer error, reverse contribution path, and constraint distance of each newly added sample are written into the sample library. When samples with the same parameter neighborhood but different solidification topology labels appear in the sample library, a segment boundary is established between the two types of samples and cross-boundary interpolation is stopped. When the low-temperature risk ranking of adjacent candidate points in the sample library is inconsistent with the ranking predicted by the local surrogate model, the corresponding area is marked as a high-error area and cross-stage calculation samples are added until the candidate parameter ranking is stably determined by the actual calculation results.

[0068] In a preferred embodiment, the low-temperature medium temperature zone includes a continuous cooling process or multiple temperature cycle processes. For a continuous cooling process, the low-temperature shrinkage mismatch value, local stress amplification value, and defect propagation driving value are accumulated according to the temperature node sequence. For multiple temperature cycle processes, the residual state is saved after each cycle and used as the initial state for the next cycle. The low-temperature risk field is characterized by the envelope value and cumulative value of the risk vector in each cycle. When tracing backward, the cycle index of the first occurrence of the risk, the cycle index of the risk reaching the envelope value, and the corresponding temperature node are retained, so that the defect formation area and the low-temperature risk amplification stage are respectively associated with the casting state source and the low-temperature temperature history source. The parameter optimization is still limited to the pouring temperature, filling speed, initial mold temperature, cooling boundary strength, and holding time sequence that can change the casting defect source.

[0069] Furthermore, all computational data is stored in association according to impeller object identifier, parameter combination identifier, stage identifier, spatial index, and time index. Each state projection saves the state before projection, the state after projection, the projection coefficient, and the conservation correction. Each reverse tracing saves the risk grid cell, candidate forming node, candidate transmission node, retained path, eliminated path, and contribution. Each directional perturbation saves the parameter action matrix, time-segmented optimization weight, perturbation direction, local sample neighborhood, and continuous confidence domain. Each cross-stage computation chain verification saves the solidified topology label, state deviation, constraint distance, and path node connection relationship. Thus, when the parameter combination changes, state transmission, risk calculation, reverse tracing, and parameter screening can be re-executed from the same data chain without relying on manual supplementation of intermediate results.

Claims

1. A method for optimizing casting parameters of a cryogenic medium centrifugal pump impeller, characterized in that, include: Acquire temporal field data of the impeller during the filling, solidification, demolding and cooling, heat treatment and low-temperature service cooling stages, and establish cross-stage grid correspondence based on a unified spatial identifier; Based on the conservation of energy, defect, and stress state, the temperature history, liquidus ratio change, solidification shrinkage, degree of insufficient feeding, compositional segregation characterization value, and residual stress state of the previous stage are projected to the next stage. Based on the low-temperature medium temperature range and cooling process, the low-temperature shrinkage mismatch value, local stress amplification value and defect propagation driving value are calculated to form a low-temperature risk field. Based on the low-temperature risk field, the defect formation area and formation time are traced in reverse, and the tracing results are converted into optimized weights for pouring temperature, filling speed, initial mold temperature, cooling boundary strength, and heat preservation sequence. The casting parameters associated with the formation period are subjected to directional perturbation according to the optimization weights, and parameter combinations that satisfy the filling constraints, solidification feeding constraints, residual stress constraints and low temperature risk constraints are selected. The establishment of the cross-stage grid correspondence includes: generating a spatial index for each stage's computational grid, consisting of impeller reference coordinates, material region identifiers, and local topology numbers; calculating the volume overlap coefficient between the source grid cells and the target grid cells for regions with inconsistent grid scales in adjacent stages, and constructing a state transfer matrix using the volume overlap coefficient; applying integral conservation projection to temperature history and liquidus rate changes, and applying peak preservation projection to the degree of insufficient feeding, compositional segregation characterization values, and residual stress state. The reverse tracing includes: constructing a grid cell risk vector according to the low-temperature shrinkage mismatch value, the local stress amplification value, and the defect propagation driving value; extracting stage reverse mapping weights from the grid correspondence between adjacent stages and the projection coefficients used for state projection, and obtaining a first reverse contribution matrix based on the stage reverse mapping weights between the low-temperature service cooling stage and the heat treatment stage; sequentially using the stage reverse mapping weights between the heat treatment stage, the demolding cooling stage, the solidification stage, and the filling stage to reverse propagate the first reverse contribution matrix; at each stage, filtering the reverse propagation results based on the liquid phase rate abrupt change location, the feeding channel connectivity status, and the main direction of residual stress to form a reverse contribution path from the low-temperature risk grid cell to the defect formation area, formation time period, and corresponding state variable, and configuring the contribution amount for each reverse contribution path; The directional perturbation includes: establishing a parameter actionable matrix based on the temporal overlap between each casting parameter in the reverse contribution path and the defect formation period; setting parameter elements that do not cover the defect formation period to 0, and setting parameter elements that cover the defect formation period and have data correlation with the state variables of the reverse contribution path to non-zero values, thereby excluding parameters that do not have an action range outside the defect formation period; distributing the contribution of the reverse contribution path to pouring temperature, filling speed, initial mold temperature, cooling boundary strength, and holding time sequence according to the parameter actionable matrix to generate time-segmented optimization weights; determining the perturbation direction and perturbation order of each parameter based on the time-segmented optimization weights, and generating candidate parameter combinations using the local proxy model that has completed the casting calculation sample construction; and processing the candidate parameter groups. The process involves performing cross-stage computation chain verification and updating the effective sample domain of the local proxy model based on the verification results. The construction of the state transfer matrix further includes: setting the impeller hub, blade root, flow channel transition region, and blade body region as independent transfer subdomains; forming an initial matrix within each transfer subdomain according to the volume overlap relationship between the source grid cell and the target grid cell; calculating the total enthalpy difference, solidification shrinkage difference, and residual stress tensor invariant difference before and after projection of the initial matrix, and decomposing each difference to the corresponding target grid cell; iteratively correcting the projection coefficients of the target grid cell using the spatial source index as a constraint until each transfer subdomain satisfies the preset conserved residual range; and configuring cross-domain correction coefficients for target grid cells located at the boundary of the transfer subdomain based on the heat flow direction of adjacent regions and the solidification front normal vector. Cross-domain correction is only performed when the spatial adjacency relationship is continuous and the material region boundary allows for heat or stress transfer; the cross-stage calculation chain verification includes: substituting the candidate parameter combination into the filling stage and solidification stage calculation, and extracting the newly generated solidification front connectivity state, feeding channel state and isolated liquid phase region distribution; When the newly generated state changes the node connection relationship of the reverse contribution path, the reverse contribution path and the time-segmented optimization weights are recalculated, and the corresponding candidate parameter combination is returned to the local proxy model for further perturbation. When the node connection relationship remains unchanged, the calculation of the demolding cooling, heat treatment and low temperature service cooling stages continues, and the consistency comparison between the projected state of each stage and the joint output variable corresponding to the candidate parameter combination is performed; only the candidate parameter combination in which the state deviation of each stage is located within the effective sample domain of the local proxy model is retained.

2. The method for optimizing casting parameters of a cryogenic medium centrifugal pump impeller according to claim 1, characterized in that, When the same target grid cell corresponds to multiple source grid cells, the projection priority is determined based on the solidification time proximity and material phase consistency, and the spatial source index and stage source index of each projection state are recorded.

3. The method for optimizing casting parameters of a cryogenic medium centrifugal pump impeller according to claim 1, characterized in that, The formation of the reverse contribution path also includes: taking the low-temperature risk grid cell as the endpoint, setting the moment when the liquid phase fraction changes from a continuous distribution to an isolated distribution during the solidification stage as a candidate formation node, and setting the moment when the cross-sectional area of ​​the feeding channel decreases as a candidate transmission node. A set of directed paths is constructed based on the spatial connectivity between the candidate forming nodes, the candidate transmission nodes and the low-temperature risk grid cells; Calculate the direct contribution of component segregation characterization value, solidification shrinkage and residual stress state to the risk vector in each directed path, as well as the indirect contribution transmitted through intermediate nodes. Directed paths whose direct and indirect contributions cancel each other out and whose combined contribution is below the path retention condition are removed, and the retained paths are sorted according to their formation time sequence.

4. The method for optimizing casting parameters of a cryogenic medium centrifugal pump impeller according to claim 1, characterized in that, The construction of the local proxy model includes: using casting parameters with non-zero weights optimized in different time periods as input variables, and using the degree of insufficient feeding, residual stress state and low temperature risk vector in the defect formation area as joint output variables; A local sample neighborhood is constructed based on the distance between the candidate parameter combination and the completed casting calculation sample, and weights are assigned to the neighborhood samples based on the consistency of the formation time of the reverse contribution path. Within the local sample neighborhood, a piecewise response surface is established between the input variable and the joint output variable. Segments whose response change direction is inconsistent with the contribution direction of the reverse contribution path are marked as mismatch segments. When generating the candidate parameter combination, the candidate points are restricted to be located within a continuous trusted domain composed of non-mismatched segments.

5. The method for optimizing casting parameters of a cryogenic medium centrifugal pump impeller according to claim 1, characterized in that, The method also includes: after completing the cross-stage calculation of the candidate parameter combination, pairing the newly calculated grid state with the corresponding projection state according to the spatial source index to form a propagation error sample; Based on the clustering location of the transmission error samples in each transmission subdomain, the transmission error volume overlap coefficient, the peak preservation projection error, and the cross-domain correction coefficient, the low-temperature risk field is regenerated using the corrected state transmission matrix and reverse tracking is performed. Compare the set of defect formation areas, the set of formation time periods, and the risk contribution ranking of each formation area before and after the correction; The weights are updated and optimized based on the tracking results where the formation area remains consistent but the risk contribution changes. The tracking results of changes in the formation region are used to redetermine the associated casting parameters, and the updated results are used for the next round of directional perturbation.

6. The method for optimizing casting parameters of a cryogenic medium centrifugal pump impeller according to claim 1, characterized in that, The method also includes: applying joint perturbations corresponding to the uncertainty intervals of the calculation input to the material thermal conductivity, latent heat of solidification, interfacial heat transfer conditions, and cooling rate of the cryogenic medium for the retained candidate parameter combinations; Under each set of joint perturbations, local proxy model prediction and cross-stage calculation chain verification are performed to obtain the set of filling state, solidification and feeding state, residual stress state and low temperature risk field corresponding to the candidate perturbation combination. Calculate the minimum distance between each set of states and the corresponding constraint boundary, and construct the joint feasibility of the candidate parameter combinations based on each minimum distance; Among the candidate parameter combinations where the node connection relationships of the reverse contribution path remain unchanged, the parameter combination with the largest joint feasibility ranking value is selected as the optimization result.

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