Grey cast iron trace element synergistic matching active optimization design method and system

Abstract

The application discloses a grey cast iron trace element synergic proportioning active optimization design method and system, and belongs to the technical field of grey cast iron smelting process parameter optimization. The method comprises the following steps: obtaining multiple initial proportioning schemes of trace elements in a grey cast iron smelting process, and constructing an initial proportioning scheme set; establishing a multi-dimensional synergic proportioning evaluation model; using a chaotic mapping sequence to disturb and amplify the initial proportioning scheme set, and generating a first generation of optimization population; performing synergic proportioning feasibility checking on individuals in the first generation of optimization population, and obtaining an effective optimization population after filtering out infeasible individuals; taking the effective optimization population as a starting generation, executing an adaptive iterative optimization process based on neighborhood competition, and outputting an optimal trace element proportioning scheme after meeting a convergence condition. The system comprises a memory and a processor, and the processor realizes the above method steps when executing a computer program.

Description

Technical Field

[0001] This invention relates to the field of gray cast iron smelting process parameter optimization technology, specifically to an active optimization design method and system for the synergistic proportioning of trace elements in gray cast iron. Background Technology

[0002] The mechanical properties of gray cast iron largely depend on the proportions of trace elements such as carbon, silicon, and manganese during the smelting process. The design of these trace element proportions is a complex decision-making problem involving multiple coupled factors. Nonlinear interactions exist between the elements, and adjusting the content of a single element alone is unlikely to yield the optimal solution for overall mechanical properties. Current methods for designing trace element proportions in gray cast iron primarily rely on the experience of process engineers and repeated trial and error. They provide approximate proportion ranges based on several known grade specifications, and then verify and fine-tune the proportion scheme through small-batch furnace tests.

[0003] This experience-driven approach to mix design struggles to systematically explore the entire space of multi-element combinations, resulting in low efficiency in generating mix design schemes. The complex mapping relationships between element ratios and mechanical properties implicit in limited historical production data fail to be fully explored and quantitatively expressed, leading to a lack of precise numerical basis for mix adjustment. When faced with new gray cast iron models or synergistic optimization requirements involving multiple performance indicators, empirical rules easily get bogged down in local feasible solutions, making it difficult to find the element combination with the optimal overall mechanical properties globally. While some existing orthogonal experiments or simple response surface methodology can formalize the relationship between mix ratios and performance, the number of mix combinations examined is limited, failing to cover the complex interaction effects between elements, resulting in mix design schemes with significant shortcomings in both optimization depth and coverage breadth.

[0004] To address the aforementioned issues, the first problem to be solved is how to break free from the constraints of the experience space based on a limited initial scheme, generating a broader and more diverse candidate matching population to provide rich foundational materials for subsequent optimization. The second problem to be solved is how to automatically adjust the search strategy based on the actual distribution of the population during iterative optimization, balancing the exploration of unknown regions with the development of known high-quality regions, and avoiding premature entrapment in local maxima. Summary of the Invention

[0005] This invention provides an active optimization design method and system for the synergistic proportioning of trace elements in gray cast iron, aiming to solve the problems of insufficient diversity of candidate solutions and fixed and rigid optimization strategies in existing experience-driven proportioning designs. By introducing a dynamic amplification mechanism based on chaotic mapping, a sufficient number of widely distributed candidate solutions are systematically generated based on the initial proportioning scheme, breaking through the limitations of human experience on the solution space. Simultaneously, an adaptive iterative optimization mechanism based on population density perception is established, actively adjusting the perturbation amplitude according to the density distribution of individuals in the search space, achieving efficient detection and precise positioning of the proportioning scheme space.

[0006] To achieve the above objectives, the present invention provides the following technical solution: In order to solve the problem that the mechanical properties are difficult to take into account and the optimization efficiency is low due to the adjustment of the trace element ratio based on experience during the gray cast iron smelting process, the present invention provides an active optimization design method and system for the synergistic ratio of trace elements in gray cast iron.

[0007] This invention discloses an active optimization design method for the synergistic proportioning of trace elements in gray cast iron, comprising: obtaining multiple initial proportioning schemes of trace elements in the gray cast iron smelting process and constructing an initial proportioning scheme set; establishing a multi-dimensional synergistic proportioning evaluation model based on the response relationship of each initial proportioning scheme to the mechanical properties of gray cast iron; perturbing and amplifying the initial proportioning scheme set using a chaotic mapping sequence to generate a first-generation optimization population; verifying the synergistic proportioning feasibility of each individual in the first-generation optimization population, filtering out infeasible individuals to obtain an effective optimization population; using the effective optimization population as the starting generation, executing an adaptive iterative optimization process based on neighborhood competition until the convergence condition is met, and outputting the optimal trace element proportioning scheme. This method combines the ergodicity of chaotic mapping with heuristic iterative optimization, actively seeking the proportion with the optimal comprehensive mechanical properties based on a multi-dimensional synergistic evaluation model while ensuring process feasibility, significantly improving optimization efficiency and global search capability.

[0008] As a preferred technical solution of the present invention, the process of establishing a multi-dimensional synergistic proportioning evaluation model specifically involves: collecting historical production data of gray cast iron including measured values ​​of tensile strength, hardness, and elongation; using the proportion of trace elements as independent variables, respectively fitting a first response surface function for tensile strength, a second response surface function for hardness, and a third response surface function for elongation; and weighted summing the three response surface functions to construct a multi-dimensional synergistic proportioning evaluation model capable of comprehensively evaluating multiple mechanical performance indicators. Preferably, the coefficients for the weighted summation are obtained using the analytic hierarchy process (AHP), and are scientifically assigned values ​​based on the process importance of each mechanical property in a specific casting, enabling the evaluation model to adapt to different working conditions.

[0009] As a preferred technical solution of the present invention, the process of generating the first-generation optimization population specifically involves: extracting the trace element composition vector of the initial proportioning scheme, the dimensions of which include carbon equivalent, silicon-carbon ratio, and mass percentage of alloying elements; using each dimension of the composition vector as an independent chaotic mapping channel, iteratively generating a chaotic perturbation sequence with the same number of dimensions using the logistic chaotic mapping formula; fusing the chaotic perturbation sequence with the corresponding initial trace element composition vector through vector addition to obtain multiple perturbed proportioning schemes with diversity and ergodicity; and merging all initial proportioning schemes and their perturbed schemes to form the first-generation optimization population. This process fully utilizes the pseudo-randomness and space-filling ability of chaotic sequences, effectively increasing the diversity of the initial population.

[0010] Furthermore, when generating the chaotic perturbation sequence, a distinct initial chaotic value is set for each dimension of the vector composed of trace elements, and iterative calculation of the logistic chaotic mapping is performed independently for each dimension. The state values ​​generated by multiple consecutive iterations are arranged to form a chaotic perturbation subsequence for that dimension, and then the subsequences of each dimension are combined into a complete chaotic perturbation sequence. Preferably, the initial chaotic value for each dimension is directly obtained by mapping the normalized ratio value of the corresponding trace element for that dimension, so that the perturbation amplitude is related to the properties of the initial scheme itself, making the perturbation more targeted.

[0011] As a preferred technical solution of the present invention, the process of verifying the feasibility of synergistic proportions is as follows: Individuals to be verified are extracted one by one from the first-generation optimization population. The proportion values ​​of each trace element are compared with the preset lower and upper limits of the process tolerance for that element. If any proportion value exceeds the range, it is directly determined as an infeasible individual. For individuals where all single-element values ​​meet the standards, the synergistic proportion constraint value between their trace elements is further calculated, and this constraint value is compared with the preset synergistic tolerance range. If it exceeds the range, it is also determined as an infeasible individual. After traversing the entire population, all undetermined feasible individuals are retained to form an effective optimization population. This dual verification mechanism prevents proportion schemes with qualified single elements but poor synergistic effects between elements from entering the optimization process, ensuring that the optimization process is always carried out within the metallurgical process window.

[0012] Furthermore, when calculating the synergistic proportion constraint value, the proportions of carbon, silicon, and manganese elements are extracted from the individual to be verified, and the carbon-silicon ratio and carbon-manganese product are calculated, which are then used together as the synergistic proportion constraint value. This set of constraint values ​​accurately reflects the synergistic influence of the main elements in gray cast iron.

[0013] As a preferred technical solution of the present invention, the adaptive iterative optimization process based on neighborhood competition specifically involves: using the current effective population as the parent generation, assigning each individual an initial neighborhood radius as the baseline radius; constructing a neighborhood space centered on each target individual, and counting the number of other individuals within it as the neighborhood density; based on the neighborhood density, dividing individuals into a sparse individual set with a density below a preset threshold and a dense individual set with a density above a preset upper limit; performing local fine perturbation operations on sparse individuals to generate the first generation of offspring individuals for in-depth exploration near potential optimal solutions; performing global coarse perturbation operations on dense individuals to generate the second generation of offspring individuals to broaden the exploration of new solution space regions; merging the two types of offspring into a new generation of population to complete one iteration. This mechanism adaptively balances local search and global exploration capabilities according to the density of the population distribution.

[0014] Furthermore, the local fine perturbation operation specifically involves: obtaining the current ratio value of each micro-element of the individual to be perturbed in the sparse set; using this value as the center, randomly generating a perturbation offset according to the preset fine perturbation step size range of the element; and superimposing the offset onto the current value to obtain a new ratio value; and combining all the new ratio values ​​to form a high-precision first-generation individual.

[0015] Furthermore, the global coarse perturbation operation specifically involves: obtaining the population center point of the current generation population where the individual to be perturbed is located in the dense set, i.e., the arithmetic mean of the ratio values ​​of each dimension; calculating the Euclidean distance between the individual to be perturbed and the population center point, and determining a global perturbation amplitude based on this distance; and randomly generating a candidate ratio value in each dimension with the value of the population center point as the center and the global perturbation amplitude as the radius, and combining all candidate values ​​to form an exploratory second generation individual.

[0016] As a preferred embodiment of the present invention, the process of determining the convergence condition and outputting the optimal solution is as follows: After each iteration, the mean value of the ratio vector of the current generation of effective population is calculated, and the absolute difference between it and the mean value of the ratio vector of the previous generation is calculated; the absolute difference is compared with a preset convergence accuracy threshold. If it is less than the threshold, the continuous stability count is accumulated; otherwise, it is cleared to zero; when the continuous stability count reaches the preset maximum number of stable counts, it is determined that the population has converged. At this time, the individual with the highest fitness value from the current generation of effective population is selected as the optimal micro-element ratio solution for output. This output solution is the process ratio with the best mechanical performance in the global scope under the current multi-dimensional target evaluation system.

[0017] This invention also includes an active optimization design system for the synergistic proportioning of trace elements in gray cast iron. The system includes a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements all steps of the aforementioned active optimization design method for the synergistic proportioning of trace elements in gray cast iron. The system can automatically execute the entire process from initial scheme acquisition, model construction, chaotic amplification, feasibility verification to adaptive iterative optimization, providing process engineers with timely and reliable optimal proportioning schemes, effectively improving the scientific nature and efficiency of gray cast iron smelting process design.

[0018] The technical effects and advantages provided by the present invention in the above technical solution are as follows: When expanding the initial matching scheme set using chaotic mapping sequences, the vector composed of the infinitesimal elements of each initial matching scheme is used as an independent information carrier. Distinct initial chaotic values ​​are assigned to each dimension, and the ergodicity and pseudo-randomness of the logistic chaotic mapping are used to independently generate chaotic perturbation sequences in each dimension. By fusing the generated chaotic perturbation sequences with the original matching vector through vector addition, a large number of perturbed matching schemes located in the neighborhood of the original schemes but not completely overlapping can be obtained. The sensitive dependence of chaotic mapping on initial conditions means that small differences in initial matching values ​​result in significantly different perturbation directions and amplitudes after iteration. The resulting group of perturbed schemes exhibits topological distribution characteristics in the matching space, maintaining correlation with the original schemes while possessing broad coverage. This expansion process does not rely on simple uniform sampling by a random number generator, but rather utilizes the inherent characteristics of deterministic nonlinear dynamical systems to generate a scheme set with space-filling capabilities. This effectively expands the candidate region that can be explored in subsequent optimization processes, avoiding the problem of insufficient scheme space coverage caused by relying solely on empirical fine-tuning or orthogonal experimental design in traditional methods.

[0019] In the adaptive iterative optimization process based on neighborhood competition, each individual in the parent population is assigned a neighborhood space with an initial baseline radius. The neighborhood density index for each individual is obtained by counting the number of individuals falling into each neighborhood space. Based on this, the population is divided into two categories: sparse and dense individual sets, which are processed separately. Individuals located in sparse regions undergo a local fine-grained perturbation operation centered on the current ratio value and based on a fine perturbation step size, causing them to shift slightly within their neighborhood space to finely explore potential high-quality solutions. For individuals located in dense regions, the global perturbation amplitude is determined based on the Euclidean distance between the individual and the population center, using the population center as a reference. A large-span global coarse-grained perturbation operation is performed in the direction towards the population periphery. This mechanism, which applies different perturbation strategies based on the local population density differences of individuals, allows the optimization process to actively escape clustering traps in dense regions and expand into insufficiently explored ratio domains, while maintaining necessary search granularity in sparse regions to ensure convergence accuracy. Throughout the iteration process, the search behavior evolves dynamically with the population distribution state. There is no need to pre-set a fixed search step size or scheduling strategy. A self-organizing balance is formed between maintaining population diversity and accelerating convergence, thereby obtaining a trace element synergistic ratio scheme that satisfies the comprehensive optimality of multiple mechanical performance indicators. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0021] Figure 1 It is a flowchart of the active optimization design method for the synergistic proportioning of trace elements in gray cast iron; Figure 2 This is a flowchart of the progeny generation process based on the optimization of trace element ratios according to neighborhood density. Figure 3 This is a flowchart for determining convergence in the iterative optimization process. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] See Figure 1This invention provides an active optimization design method for the synergistic proportioning of trace elements in gray cast iron. The method obtains multiple initial proportioning schemes and constructs a set. Based on the response relationship of the proportioning schemes to mechanical properties, a multidimensional synergistic proportioning evaluation model is established. The initial schemes are perturbed and amplified using a chaotic mapping sequence to generate a first-generation optimization population. The synergistic proportioning feasibility of the population individuals is checked to filter out infeasible individuals to obtain an effective optimization population. Then, an adaptive iterative optimization process based on neighborhood competition is executed with the effective optimization population as the starting generation. After the convergence condition is met, the optimal trace element proportioning scheme is output.

[0024] In practice, historical production data for gray cast iron is collected. Each historical production data point includes a set of historical micronutrient ratio schemes and the corresponding measured values ​​of tensile strength, hardness, and elongation. The historical micronutrient ratio schemes include the ratios of carbon, silicon, manganese, and sulfur.

[0025] Using the proportions of each trace element in the historical trace element formulation as independent variables and the measured tensile strength as the dependent variable, the first response surface function was fitted using a multiple quadratic regression method. ,in, This represents the vector of independent variables composed of the proportions of various trace elements. The process of the multiple quadratic regression method is as follows: A polynomial model containing linear, quadratic, and interaction terms is established; the coefficients in the polynomial model are estimated using the least squares method to minimize the sum of squared residuals between the polynomial model output and the measured tensile strength; after solving for the polynomial coefficients, the first response surface function is obtained. The complete expression. To fit the first response surface function. Same independent variable vector Using the measured hardness value as the dependent variable, the second response surface function was fitted using the same multiple quadratic regression method as described above. The first response surface function is fitted with the given function. Same independent variable vector Using the measured elongation as the dependent variable, the same multiple quadratic regression method as described above was used to fit the third response surface function. .

[0026] The first response surface function Second response surface function and the third response surface function We perform weighted summation to construct a multi-dimensional synergistic ratio evaluation model. Multidimensional synergistic ratio evaluation model The expression is:

[0027] in, This represents a vector representing the proportions of trace elements. Each component corresponds to a specific ratio of trace elements. This represents the first response surface function, used to determine the proportions of trace elements based on the vector. Calculate the predicted tensile strength; This represents the second response surface function, used to determine the micro-element ratio vector. Calculate the predicted hardness value; This represents the third response surface function, used to determine the proportions of trace elements. Calculate the predicted elongation value; Represents the corresponding first response surface function The weighting coefficients, Represents the corresponding second response surface function The weighting coefficients, Represents the corresponding third response surface function Weighting coefficients, weighting coefficients , and satisfy .

[0028] Weighting coefficients , and The Analytic Hierarchy Process (AHP) was used to assign values ​​to tensile strength, hardness, and elongation based on their process importance. The AHP assignment process involved: establishing a hierarchical model where the target layer represents the optimal mechanical properties of gray cast iron, and the criterion layers included tensile strength, hardness, and elongation criteria; and constructing pairwise comparison judgment matrices based on the process importance of the three criteria. The elements in these judgment matrices were denoted as... , Indicates the first The first criterion is relative to the first The importance of each criterion The values ​​are taken using a scale of 1 to 9. Indicates the first The first criterion and the first Each criterion is equally important. Indicates the first The first criterion is compared to the second. This criterion is extremely important; calculate the largest eigenvalue of the judgment matrix and the corresponding normalized eigenvector, and use the three components of the normalized eigenvector as weighting coefficients in turn. , and The value of is taken; a consistency test is performed on the judgment matrix, and the consistency ratio is calculated. When the consistency ratio is less than 0.1, the judgment matrix is ​​considered to have passed the consistency test. The weighting coefficient is then used. , and If the value is valid, otherwise the elements in the judgment matrix are readjusted. Until the consistency check is passed.

[0029] In practical implementation, a trace element composition vector is extracted from the set of initial proportioning schemes for each initial proportioning scheme. Each trace element composition vector contains the carbon equivalent proportion, silicon-carbon ratio proportion, and mass percentage proportion of alloying elements. The number of dimensions of the trace element composition vector is denoted as... , The value of is a positive integer. A vector is formed using infinitesimal elements. This represents the vector of infinitesimal elements for any initial mixing scheme. The Middle The trace element ratio values ​​in each dimension are denoted as , The value is from arrive All integers.

[0030] For the vector composed of trace elements The first in Dimension 1, obtain the 1st dimension The corresponding process tolerance lower limit values ​​for each dimension and process allowable upper limit ,in, Less than Using the process allowable lower limit value and process allowable upper limit Micronutrient ratio Normalization is performed, and the calculation method for normalization is as follows: , Indicates the first The normalized ratio values ​​corresponding to each dimension The value is located in the interval Within. Normalize the proportions. As the first The initial chaotic value of each dimension is denoted as . Due to the different proportions of trace elements in different dimensions Process allowable lower limit and process allowable upper limit Different from all Initial values ​​of chaos in each dimension They are not the same.

[0031] Preset number of chaos iterations , greater than positive integers, The value is determined based on the number of perturbation-induced proportioning schemes to be generated. Preset chaos control parameters. , The value is , The value of makes the logistic chaotic mapping state completely chaotic. A vector is formed from the infinitesimal elements. The first in Each dimension independently performs iterative calculations of the logistic chaotic map. The iterative formula for the logistic chaotic map is:

[0032] in, Indicates the first The dimension in the first Chaotic state values ​​generated in the next iteration. The iteration number, The value is from arrive All integers; Indicates the first The dimension in the first The chaotic state value of the next iteration, when hour, For the first Initial values ​​for chaos in each dimension; This represents the chaos control parameters. From... Begin by repeatedly executing the above iterative formula until... , obtained the Each dimension corresponds to The chaotic state values ​​are ordered in ascending order of iteration number. Each dimension The arrangement of the chaotic state values ​​constitutes the first chaotic state value. The chaotic perturbation subsequences corresponding to each dimension are denoted as . , The elements contained therein are, in order: .

[0033] In practical implementation, the vector is composed of trace elements. Perform the above operation on each dimension to obtain all Each dimension corresponds to a chaotic perturbation subsequence. All The chaotic perturbation subsequences of each dimension are combined in ascending order of dimension number to form a chaotic perturbation sequence, denoted as [equation]. Chaotic perturbation sequence For one OK Column data structure, chaotic perturbation sequence The Middle Line number The element of the column is the first The first dimension chaotic state values .

[0034] For chaotic perturbation sequences For each iteration number Extracting chaotic perturbation sequences The Middle All elements of the column constitute a perturbation offset vector, denoted as . , The elements contained therein are, in order: The perturbation offset vector Vectors composed of trace elements Vector addition fusion is performed by combining infinitesimal elements into a vector. The Middle Trace element ratios in each dimension With the disturbance offset vector The Middle Chaotic state values ​​in each dimension By adding elements one by one, we obtain the perturbed ratio. .all Perturbation ratio values ​​in each dimension This forms a perturbation-resolved allocation vector, denoted as [missing information]. , This corresponds to a perturbation-induced allocation scheme. Take, in sequence... , co-generated Different perturbation offset vectors and generate accordingly A perturbation-based allocation scheme.

[0035] In practical implementation, for each initial proportion scheme in the initial proportion scheme set, all the operations described above—extracting trace elements to form a vector, setting initial chaotic values, iteratively generating chaotic perturbation subsequences, combining chaotic perturbation sequences, and vector addition fusion—are performed. Each initial proportion scheme generates... Each initial ratio scheme is perturbed. The vectors of all original trace elements of all initial ratio schemes are merged with the vectors of all perturbed ratios corresponding to all initial ratio schemes to form the first generation of the optimization population. Each individual in the first generation of the optimization population corresponds to a trace element ratio vector.

[0036] In practice, an individual to be verified is extracted from the first-generation optimization population, and this individual is represented as a trace element ratio vector. The ratio values ​​of each trace element in the trace element ratio vector are read, including the ratio values ​​of carbon, silicon, manganese, and sulfur.

[0037] For each trace element, a lower and upper limit for process tolerance are preset. The lower limit for carbon is denoted as... The upper limit of carbon element processing is denoted as The minimum allowable limit for silicon element processing is denoted as... The upper limit of silicon element processing is denoted as The minimum allowable limit for manganese in processes is denoted as... The upper limit of manganese content in the process is denoted as The minimum allowable limit for sulfur in the process is denoted as... The upper limit of sulfur content in the process is denoted as .in, Less than , Less than , Less than , Less than The aforementioned lower and upper limits of the process tolerance are preset based on the gray cast iron smelting process specifications and production equipment capacity, and are stored in the system configuration parameters.

[0038] The carbon element ratio in the individual to be verified is compared with the lower limit of carbon element allowable by the process. And the upper limit of carbon element process If the carbon element ratio is less than Or the carbon element ratio is greater than If the carbon element ratio value is within the range, the individual to be verified is determined to be infeasible, and subsequent verification operations for the individual to be verified are terminated. Within this range, the silicon element ratio and the allowable lower limit of silicon element in the process will continue to be maintained. And the upper limit of silicon element process If the silicon element ratio is less than Or the silicon element ratio is greater than If the individual to be verified is found to be infeasible, then the same method is used to compare the process tolerance ranges corresponding to the manganese and sulfur element ratios. If the ratio of any trace element exceeds the range defined by the lower and upper limits of the corresponding process tolerance, the individual to be verified is determined to be infeasible.

[0039] In some implementations, when all trace element ratios are within their respective process tolerance ranges, the synergistic ratio constraints among trace elements in the individual to be verified are further calculated. The carbon element ratio is then extracted from the individual to be verified. Silicon element ratio ratio of manganese element ,in This represents the mass percentage of carbon in the individual being tested. This represents the mass percentage of silicon in the individual being tested. This represents the mass percentage of manganese in the individual being tested. Calculate the carbon content. Silicon element ratio The ratio of carbon to silicon ratio constraint value is obtained. Carbon-silicon ratio constraint value The calculation formula is:

[0040] in, This indicates the carbon element ratio. Indicates the silicon element ratio. This indicates the carbon-silicon ratio constraint value.

[0041] In calculating the carbon-silicon ratio constraint value At the same time, calculate the carbon element ratio. Ratio with manganese The product of the two is used to obtain the carbon-manganese product constraint value. Carbon-manganese product constraint value The calculation method is as follows The carbon-silicon ratio constraint value Carbon-manganese product constraint value Together they serve as the constraint value for synergistic proportioning.

[0042] In some implementations, the synergistic ratio constraint value needs to be compared with a preset synergistic tolerance range. The synergistic tolerance range includes a lower limit for the carbon-silicon ratio. The maximum allowable value for carbon-silicon ratio And the permissible lower limit of carbon and manganese volume. The maximum allowable value of carbon-manganese product The permissible lower limit for carbon-silicon ratio The maximum allowable value for carbon-silicon ratio Based on the pre-determined requirements for graphite morphology control according to the metallographic structure of gray cast iron, the allowable lower limit value of carbon-manganese product is determined. The maximum allowable value of carbon-manganese product The content of pearlite in gray cast iron and the matrix strengthening effect are determined in advance.

[0043] Carbon-silicon ratio constraint value The lower limit of the ratio of carbon to silicon The maximum allowable value for carbon-silicon ratio If a comparison is made, Less than or Greater than If the value is not specified, the individual to be verified is determined to be infeasible. The carbon-manganese product constraint value is then used. The lower limit of carbon-manganese product The maximum allowable value of carbon-manganese product If a comparison is made, Less than or Greater than If the carbon-silicon ratio constraint value is not met, the individual to be verified is determined to be an infeasible individual. Located within the permissible range of carbon-silicon ratio Within, and the carbon-manganese product constraint value Located within the allowable range of carbon and manganese volume Within this timeframe, the individual to be verified will not be deemed an infeasible individual.

[0044] In practice, all individuals in the first-generation optimization population are traversed, and the aforementioned collaborative matching feasibility verification steps are performed on each individual. An empty set of reserved individuals is created, and individuals not determined to be infeasible are added to this set. After the traversal is complete, all individuals in the reserved set constitute the effective optimization population.

[0045] In specific implementation, please refer to Figure 2 The current generation of effective optimization population is used as the parent population, and the parent population contains Each individual is represented as a vector composed of infinitesimal elements, and the total dimension of the vector composed of infinitesimal elements is denoted as . , The value is a positive integer. A neighborhood radius is assigned to each individual in the parent population, with the initial value of the neighborhood radius being a preset baseline radius. Preset baseline radius The value of is determined based on the average distance between individuals in the trace element sizing space, and all dimensions of the trace element composition vector have been normalized to the interval. In this case, The value is set to .

[0046] For each target individual in the parent population, the neighborhood radius assigned to the target individual is... Using a radius, construct the neighborhood space of the target individual. The neighborhood space is defined as the Euclidean distance between the target individual and the microelement sizing space that is less than or equal to... The region comprised of all points. The number of individuals in the parent population (excluding the target individual) falling into the target individual's neighborhood is counted, and this number is taken as the target individual's neighborhood density. The target individual's neighborhood density is denoted as... .

[0047] In practice, a density threshold is set in advance. and density upper limit , The value is less than The value of density threshold. The value is determined by the size of the parent population. and neighborhood radius Together, it was determined that when the parental population size When the value is between 50 and 200, the density threshold The value is 3, which is the upper limit of density. The value is set to 8. This represents the neighborhood density corresponding to each target individual in the parent population. With density threshold and density upper limit Compare them. If the neighborhood density of the target individual... Less than the density threshold If the target individual is included in the sparse individual set, then the target individual is classified into the sparse individual set. If the neighborhood density of the target individual... Greater than the upper limit of density If the target individual is found to be a specific individual, it is classified into the dense individual set. After traversing all individuals in the parent population, a sparse individual set consisting of all individuals whose neighborhood density is below the density threshold and a dense individual set consisting of all individuals whose neighborhood density is above the density upper limit are obtained.

[0048] In some implementations, a local fine-grained perturbation operation is performed on each individual to be perturbed in the sparse individual set. One individual to be perturbed is selected from the sparse individual set, and the current value of the microelement ratio for each microelement in that individual is obtained. The current value of the trace element ratio is denoted as , The value ranges from 1 to Regarding the first For each trace element, a fine perturbation step size range is preset, the first... The fine perturbation step size range for each trace element is denoted as ,in, Indicates the first The maximum step size of fine perturbation of each trace element. The value is based on the first The allowable local adjustment range for each trace element in the process, for carbon, is set. The value is the mass percentage of carbon. For silicon, The value is the mass percentage of silicon. For manganese, The value is the mass percentage of manganese. Within the aforementioned fine perturbation step size range Within, perturbation offsets are generated through uniform random sampling. Disturbance offset satisfy The disturbance offset Added to the current value Above, obtain the perturbation ratio value. Treating all disturbed individuals The above superposition operation is performed on each trace element to obtain... After perturbation, all the perturbation ratios are combined into a new individual, which becomes a member of the first generation of individuals. A local fine perturbation operation is performed on each individual to be perturbed in the sparse individual set, generating the same number of first-generation individuals as the total number of individuals in the sparse individual set.

[0049] In some implementations, a global coarse-grained perturbation operation is performed on each individual to be perturbed in the dense set of individuals. One individual to be perturbed is selected from the dense set, and the population centroid of the current generation's effective optimization population containing that individual is obtained. The population centroid is represented as a vector. ,vector The Middle The numerical values ​​of each dimension It is the total number of individuals in the current generation of the effective optimization population in the th... The arithmetic mean of the proportions of each trace element is calculated. The trace element composition vector of the individual to be perturbed is then calculated. With the population center Euclidean distance between Euclidean distance The calculation formula is:

[0050] in, This represents the total number of dimensions of the vector composed of infinitesimal elements; The vector representing the micro-element composition of the individual to be disturbed. The proportions of each dimension; The first point in the population centroid vector represents the... The numerical value of the dimension, that is, the total number of individuals in the current generation of the effective optimization population at the . The arithmetic mean of the proportions of each trace element; This represents the Euclidean distance between the vector of trace elements of the individual to be disturbed and the population center.

[0051] According to Euclidean distance Determine the global perturbation amplitude of the individual to be perturbed Global disturbance amplitude Euclidean distance A positive correlation exists. In practical implementation, the global disturbance amplitude... according to Calculate, where, This represents the global disturbance coefficient. The value is set to Global perturbation coefficient Set as The basis is to ensure that the global disturbance amplitude can effectively jump out of dense areas in the search space without disturbing invalid areas. This is based on the analysis of the spatial distribution characteristics of trace element proportions. It can balance the needs of exploration and convergence.

[0052] In each dimension of the vector composed of trace elements, with the population center point as the guide... The numerical values ​​of each dimension Centered on the global disturbance amplitude Generate candidate ratio values ​​with radius. Candidate ratio values The generation method is in the interval Uniform random sampling is performed within the area. All Candidate matching values ​​in each dimension The individuals are combined to form a new individual, which becomes a member of the second generation of individuals. A global coarse perturbation operation is performed on each individual to be perturbed in the dense individual set, and the number of second generation individuals generated is the same as the number of individuals in the dense individual set.

[0053] In practice, the first and second offspring individuals are merged to form the offspring population, which is the next generation of effective optimization population obtained after one iteration of optimization.

[0054] In specific implementation, please refer to Figure 3 After each adaptive iterative optimization process, the current generation of effective optimization population is obtained. The current generation of effective optimization population contains... There are 10 individuals, each represented as a matching vector, and the total number of dimensions of the matching vectors is denoted as . , The value of is a positive integer. Calculate the arithmetic mean of the proportions of all individuals in the current generation's effective optimization population across each dimension, and then... The vector composed of the arithmetic mean of each dimension is used as the mean of the matching vector of the current generation of effective optimization population. The mean of the matching vector of the effective search population is denoted as ,in This represents the algebraic number of the adaptive iterative optimization process. The value of is a positive integer. The Middle The values ​​of each dimension represent all the values ​​in the current generation of the effective optimization population. The individual in the first The arithmetic mean of the proportions in each dimension The value is from arrive All integers.

[0055] After calculating the mean of the matching vector for the current generation, read the mean of the matching vector of the previous generation's effective optimization population. The mean of the matching vector of the previous generation of effective optimization population The calculations were completed and stored at the end of the previous iteration optimization process. The absolute difference between the mean of the matching vectors of the current generation of effective optimization population and the previous generation of effective optimization population is calculated; this absolute difference is denoted as... absolute difference The calculation formula is:

[0056] in, The total number of dimensions of the balancing vector; Indicates the first Mean of the matching vector of an effective search population The Middle The values ​​of each dimension; Indicates the first Mean of the matching vector of an effective search population The Middle The values ​​of each dimension; Indicates the first Effective search for optimal populations and the first generation The absolute difference between the mean values ​​of the matching vectors of the effective optimization population.

[0057] In practice, a convergence accuracy threshold is preset. Convergence accuracy threshold The value is Convergence accuracy threshold The value is set to The basis for this is that the ratio of trace elements is usually accurate to four decimal places during process adjustments. When the absolute difference between the mean values ​​of the ratio vectors of two generations of populations is less than this order of magnitude, the population has no substantial change in the ratio scheme, indicating that the optimization process has converged to a stable region.

[0058] absolute difference With convergence accuracy threshold Compare them. If the absolute difference... Less than the convergence accuracy threshold For continuous stable count values Perform an accumulation operation to obtain a continuous and stable count value. The update method is If the absolute difference Greater than or equal to the convergence accuracy threshold For continuous stable count values Perform a zeroing operation to achieve a continuous and stable count value. The update method is Continuous stable count value The initial value is Initialization settings are performed before the adaptive iterative optimization process begins.

[0059] In practice, the maximum number of consecutive stable cycles is preset. Maximum number of consecutive stable cycles The value is Maximum number of consecutive stable cycles The value is set to The basis for this is that during the iterative optimization process, the mean of the population matching vector may become stable once or twice due to random disturbances. Five consecutive stable values ​​indicate that the population has entered a continuous convergence state, which can effectively avoid false convergence judgments caused by random fluctuations.

[0060] In each update of the continuous stable count value Then, the updated continuous stable count value will be... With the maximum number of consecutive stable times Compare. When the count values ​​are continuously stable. Reaching the maximum number of consecutive stable times When the convergence condition is met, the fitness value of each individual in the current generation of the effective optimization population is obtained. The fitness value of each individual is calculated by the multidimensional collaborative matching evaluation model, which takes the individual's matching vector as input and outputs the corresponding fitness value. The individual with the highest fitness value in the current generation of the effective optimization population is selected as the optimal microelement matching scheme, and the matching values ​​of each microelement in the optimal microelement matching scheme are output. When the continuous stable count value Maximum number of consecutive stable cycles not reached If the convergence condition is not met, the subsequent adaptive iterative optimization process continues.

[0061] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. An active optimization design method for the synergistic proportioning of trace elements in gray cast iron, characterized in that, Includes the following steps: Obtain multiple initial proportioning schemes of trace elements in the gray cast iron smelting process, and construct a set of initial proportioning schemes; Based on the response relationship of each trace element initial proportion scheme to the mechanical properties of gray cast iron, a multi-dimensional synergistic proportion evaluation model is established. The initial allocation scheme set is perturbed and expanded using a chaotic mapping sequence to generate a first-generation optimization population; The feasibility of cooperative matching is verified for each individual in the first generation of the optimization population. After filtering out infeasible individuals, an effective optimization population is obtained. Using the effective optimization population as the starting generation, an adaptive iterative optimization process based on neighborhood competition is executed until the convergence condition is met, at which point the optimal micro-element ratio scheme is output.

2. The active optimization design method for the synergistic proportioning of trace elements in gray cast iron according to claim 1, characterized in that, The specific steps for establishing a multidimensional synergistic proportioning evaluation model based on the response relationship of each trace element initial proportioning scheme to the mechanical properties of gray cast iron are as follows: Collect historical production data of gray cast iron. Each historical production data includes a set of historical trace element ratio schemes and their corresponding measured values ​​of tensile strength, hardness and elongation. Using the proportions of each trace element in the historical trace element formulation as the independent variable and the measured tensile strength as the dependent variable, the first response surface function is fitted. Using the same independent variable and the measured hardness value as the dependent variable, fit the second response surface function; Using the same independent variable and the measured elongation as the dependent variable, fit the third response surface function; The first response surface function, the second response surface function, and the third response surface function are weighted and summed to construct the multidimensional synergistic ratio evaluation model.

3. The active optimization design method for the synergistic proportioning of trace elements in gray cast iron according to claim 2, characterized in that, The weighting coefficients in the weighted summation are assigned values ​​based on the process importance of tensile strength, hardness, and elongation using the analytic hierarchy process (AHP).

4. The active optimization design method for the synergistic proportioning of trace elements in gray cast iron according to claim 1, characterized in that, The specific steps for perturbing and expanding the initial matching scheme set using a chaotic mapping sequence to generate the first-generation optimization population are as follows: Extract the trace element composition vector of each initial proportion scheme from the set of initial proportion schemes. Each trace element composition vector includes carbon equivalent, silicon-carbon ratio and mass percentage of alloying elements. Using each dimension of the vector composed of the trace elements as an independent chaotic mapping channel, a chaotic perturbation sequence with the same number of dimensions as the vector composed of the trace elements is generated iteratively using the logistic chaotic mapping formula. The chaotic perturbation sequence and the corresponding trace element vector are fused by vector addition to obtain multiple perturbation ratio schemes; All initial proportion schemes and their corresponding perturbation-induced proportion schemes are merged to form the first generation of optimization population.

5. The active optimization design method for the synergistic proportioning of trace elements in gray cast iron according to claim 4, characterized in that, The specific steps for iteratively generating a chaotic perturbation sequence with the same number of dimensions as the vector composed of the infinitesimal elements using the logistic chaotic mapping formula are as follows: A chaotic initial value is set for each dimension of the vector composed of the trace elements, and the chaotic initial values ​​of all dimensions are different. For each dimension, the iterative calculation of the logistic chaotic map is performed independently, and a chaotic state value is generated in each iteration; Arrange the chaotic state values ​​generated by multiple consecutive iterations in the order of iteration to form a chaotic perturbation subsequence corresponding to that dimension. The chaotic perturbation subsequences of each dimension are combined in dimensional order to form the chaotic perturbation sequence.

6. The active optimization design method for the synergistic proportioning of trace elements in gray cast iron according to claim 5, characterized in that, The initial chaotic value set for each dimension is obtained by using the normalized ratio of the corresponding trace element as the initial value.

7. The active optimization design method for the synergistic proportioning of trace elements in gray cast iron according to claim 1, characterized in that, The specific steps for verifying the feasibility of cooperative matching for each individual in the first-generation optimization population and filtering out infeasible individuals to obtain an effective optimization population are as follows: Extract an individual to be verified from the first generation of the optimization population, and read the ratio of each trace element in the individual to be verified. The ratio of each trace element is compared with the preset lower and upper limits of the process tolerance for that trace element. If any ratio exceeds the range defined by the corresponding lower and upper limits, the individual to be verified is determined to be an infeasible individual. If all ratio values ​​are within the corresponding interval range, then the synergistic ratio constraint value between trace elements in the individual to be verified is further calculated, and the synergistic ratio constraint value is compared with the preset synergistic tolerance range. If it exceeds the synergistic tolerance range, it is determined to be an infeasible individual. Traverse all individuals in the first generation of the optimization population, and retain all individuals that have not been determined to be infeasible individuals to form the effective optimization population.

8. The active optimization design method for the synergistic proportioning of trace elements in gray cast iron according to claim 1, characterized in that, Using the aforementioned effective optimization population as the starting generation, the specific steps for performing an adaptive iterative optimization process based on neighborhood competition are as follows: The current generation of effective optimization population is used as the parent population. Each individual in the parent population is assigned a neighborhood radius, and the initial value of the neighborhood radius is a preset benchmark radius. For each target individual in the parent population, a neighborhood space is constructed with the target individual as the center and the neighborhood radius of the target individual as the radius. The number of other individuals falling into the neighborhood space is counted as the neighborhood density of the target individual. Based on the neighborhood density of each target individual, individuals with neighborhood densities lower than a preset density threshold are selected from the parent population to form a sparse individual set, while individuals with neighborhood densities higher than a preset density upper limit are selected to form a dense individual set. For each individual in the sparse individual set, a local fine perturbation operation is performed to generate a first generation individual. For each individual in the dense individual set, a global coarse perturbation operation is performed to generate a second generation individual. The first generation individual and the second generation individual are merged to form the offspring population, thus completing one iteration of optimization.

9. The active optimization design method for the synergistic proportioning of trace elements in gray cast iron according to claim 1, characterized in that, The specific steps for outputting the optimal trace element ratio scheme after the convergence condition is met are as follows: After each adaptive iterative optimization process is completed, the mean of the matching vector of all individuals in the current generation of effective optimization population is calculated, and the absolute difference between the mean of the matching vector of the current generation of effective optimization population and the mean of the matching vector of the previous generation of effective optimization population is calculated. The absolute difference is compared with a preset convergence accuracy threshold. If the absolute difference is less than the convergence accuracy threshold, the continuous stable count value is incremented by one; otherwise, the continuous stable count value is cleared to zero. When the continuous stable count value reaches the preset maximum number of continuous stable counts, it is determined that the convergence condition is met, and the individual with the highest fitness value in the current generation of effective optimization population is output as the optimal trace element ratio scheme.

10. An active optimization design system for the synergistic proportioning of trace elements in gray cast iron, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the active optimization design method for the synergistic proportioning of trace elements in gray cast iron as described in any one of claims 1 to 9.

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