Project problem solving method and system based on constitutive model driving

Abstract

The invention relates to the technical field of data processing, and provides an engineering problem solving method and system based on constitutive model driving, and the method comprises the steps: carrying out the physical item mining of priori knowledge, and obtaining a candidate constitutive item set; performing data enhancement on the experimental data through a Gaussian noise function to obtain an expanded training data set; performing nested optimization on the candidate constitutive item set to obtain an optimal constitutive equation structure and parameter combination; according to a multi-target screening criterion, carrying out interpretability verification on the optimal constitutive equation structure and the parameter combination, and establishing and obtaining an engineering problem constitutive model; and solving a to-be-solved engineering problem through the engineering problem constitutive model to obtain a solving result. According to the construction method for the high-precision constitutive model of the engineering problem, the automatic construction of the interpretable engineering constitutive model is realized, and the prediction accuracy is improved.

Description

Technical Field

[0001] The present invention belongs to the field of data processing technology, and in particular relates to a method and system for solving engineering problems driven by a constitutive model. Background Art

[0002] Current data-driven AI models, such as machine learning and large language models, have shown great potential in solving engineering problems. These models construct complex nonlinear mapping relationships through massive amounts of data and are able to handle multi-variable, multi-constraint engineering optimization problems that are difficult to solve with traditional numerical methods. In the fields of materials science, structural engineering, thermal conductivity analysis, etc., prediction models based on deep neural networks have been widely used in performance prediction, parameter optimization, and simulation calculations. At the same time, in order to enhance the physical rationality of the model, researchers have proposed improved methods that integrate physical laws, such as physical information neural networks, in an attempt to introduce physical constraints while maintaining high accuracy. These methods alleviate the limitations of pure data-driven models to a certain extent by embedding partial differential equations or physical laws in the loss function.

[0003] However, existing technical solutions still have significant shortcomings: First, the black box characteristics of traditional AI models make the decision logic completely untraceable, and engineers cannot understand the internal reasoning process of the model, which seriously hinders the deepening of disciplinary mechanism cognition and the improvement of model credibility; Second, existing physical information fusion methods overly rely on explicit physical formulas and mandatory constraint optimization paths. In complex engineering scenarios where there is no complete theoretical basis or the physical mechanism is not yet fully understood, these methods are difficult to achieve high-precision modeling; Third, when dealing with complex engineering problems such as multi-physical field coupling and cross-scale effects, current methods often require a lot of prior knowledge and manual parameter adjustment, have a low degree of automation, and it is difficult to build reliable prediction models under limited experimental data conditions. Summary of the Invention

[0004] In view of the above deficiencies in the prior art, the purpose of the present invention is to provide a method and system for solving engineering problems driven by a constitutive model.

[0005] The first aspect of the present invention provides a method for solving engineering problems driven by a constitutive model, comprising: S1: Mining physical terms from prior knowledge to obtain a set of candidate constitutive terms; S2: Perform data enhancement on the experimental data through Gaussian noise function to obtain an expanded training data set; S3: performing nested optimization on the candidate constitutive term set to obtain the optimal constitutive equation structure and parameter combination; S4: verifying the interpretability of the optimal constitutive equation structure and the parameter combination, and establishing a constitutive model of the engineering problem based on the verified optimal constitutive equation structure and parameter combination; S5: Solve the engineering problem to be solved by using the engineering problem constitutive model to obtain a solution result.

[0006] According to the constitutive model-driven engineering problem solving method provided by the present invention, step S1 further includes: S11: Determine relevant variable parameters based on the target quantity of the engineering problem; S12: Combine related variables into local physical terms; S13: Add exponential functions to multiple local physical terms to perform dimension elimination and obtain a standardized set of candidate constitutive terms.

[0007] According to the constitutive model-driven engineering problem solving method provided by the present invention, the candidate constitutive term set in step S1 is selected according to the physical mechanism of the engineering field corresponding to the engineering problem to be solved.

[0008] According to the engineering problem solving method based on constitutive model driving provided by the present invention, step S3 further includes: S31: performing an outer structure search on the candidate constitutive term set by a symbolic regression algorithm to obtain a candidate formula structure set; S32: Optimizing inner parameters of multiple formulas in the candidate formula structure set using a differential optimization algorithm to obtain optimal parameter configurations for the multiple formulas; S33: Performing a performance evaluation on the optimal parameter configuration according to a cross entropy loss function and regularization constraints to obtain an optimal constitutive equation structure and parameter combination.

[0009] According to the constitutive model-driven engineering problem solving method provided by the present invention, the differential optimization algorithm in step S32 adopts the best1bin strategy.

[0010] According to the engineering problem solving method based on constitutive model driving provided by the present invention, step S4 further includes: S41: Physical constraint verification is used to verify the physical rationality of the optimal constitutive equation structure and parameter combination, and obtain the physical constraint verification results; S42: Based on the accuracy index and the physical constraint verification results, the optimal constitutive equation structure and parameter combination are evaluated to obtain a constitutive model for the engineering problem.

[0011] According to a constitutive model-driven engineering problem solving method provided by the present invention, the engineering problem to be solved in step S5 includes: Process parameter optimization problems, cross-scale performance prediction problems, and finite element simulation problems.

[0012] A second aspect of the present invention provides an engineering problem solving system driven by a constitutive model, comprising: Mining module: used to mine physical terms from prior knowledge and obtain a set of candidate constitutive terms; Enhancement module: used to enhance the experimental data through Gaussian noise function to obtain an expanded training data set; Optimization module: used to perform nested optimization on the candidate constitutive term set to obtain the optimal constitutive equation structure and parameter combination; Verification module: used to verify the interpretability of the optimal constitutive equation structure and the parameter combination, and establish a constitutive model of the engineering problem based on the verified optimal constitutive equation structure and parameter combination; A solution module is configured as the constitutive model of the engineering problem established by the verification module, and is used to solve the engineering problem to be solved and obtain a solution result.

[0013] A third aspect of the present invention provides an engineering problem solving device driven by a constitutive model, comprising: a memory and at least one processor, wherein instructions are stored in the memory; At least one of the processors calls the instructions in the memory to enable a constitutive model-driven engineering problem solving device to execute any one of the constitutive model-driven engineering problem solving methods described above.

[0014] A fourth aspect of the present invention provides a computer-readable storage medium having instructions stored thereon, which, when executed by a processor, implement a constitutive model-driven engineering problem solving method as described above.

[0015] The present invention provides a constitutive model-driven engineering problem-solving method and system, which uses a large language model to perform physical item mining on engineering problem-related literature and prior knowledge. It can systematically extract and integrate physical mechanism information scattered in massive literature, avoiding the limitations of traditional methods that rely on personal experience and subjective judgment, significantly improving the comprehensiveness and accuracy of physical item identification, and providing a richer and more reliable physical foundation for subsequent modeling.

[0016] The present invention performs data enhancement processing on a small amount of experimental data through Gaussian noise function, effectively solving the key problem of scarce experimental data in engineering practice. It expands a small amount of original data into a large number of training samples, which not only greatly reduces the experimental cost and time investment, but also can fully explore the potential information in the limited data, so that the model can still achieve high-precision prediction effects under small sample conditions, providing a realistic and feasible solution for resource-constrained engineering projects.

[0017] Secondly, the present invention also performs nested optimization processing on the candidate constitutive term set through symbolic regression algorithm and differential optimization algorithm, realizing the coordinated evolution of formula structure search and parameter optimization. The outer symbolic regression algorithm can efficiently search for the optimal structure combination in the huge formula space, and the inner differential optimization algorithm ensures that each candidate formula can find the local optimal parameter configuration. The two-layer optimization strategy not only improves the global search efficiency, but also ensures that the mathematical expression of the final model is consistent with physical intuition and has the best fitting performance.

[0018] In addition, the present invention performs performance evaluation on each formula based on the cross-entropy loss function and regularization constraints, effectively balancing the relationship between model complexity and prediction accuracy, preventing overfitting, ensuring that the model has good generalization ability, and performing rationality testing on the optimal constitutive equation through physical constraint verification to ensure that the generated mathematical model not only performs well in a statistical sense, but more importantly, maintains rationality and interpretability in a physical sense, enabling engineers to intuitively understand the model's prediction logic and physical mechanism, thereby enhancing the model's credibility and practicality.

[0019] Overall, the constitutive model constructed in the present invention can be directly applied to multiple engineering fields such as process parameter optimization, cross-scale performance prediction, and finite element simulation calculations. It provides a highly accurate and interpretable prediction tool for complex engineering problems, promotes the transformation of engineering science from experience-driven to theory-guided, and has important scientific value and engineering application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The accompanying drawings are only for the purpose of illustrating specific embodiments and are not to be considered as limiting the present invention. Throughout the drawings, the same reference numerals represent the same components. Obviously, the drawings described below are only some of the embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings.

[0021] Figure 1 A schematic diagram of a method flow for solving an engineering problem based on a constitutive model driven method provided by an embodiment of the present invention; Figure 2 A schematic diagram of a method and device for solving engineering problems driven by a constitutive model provided in an embodiment of the present invention.

[0022] Reference numerals: 100, mining module; 200, enhancement module; 300, optimization module; 400, verification module; 500, solution module. DETAILED DESCRIPTION

[0023] In order to enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are part of the embodiments of the present invention, rather than all of the embodiments. It should be understood that these descriptions are merely exemplary and are not intended to limit the scope of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative work should fall within the scope of protection of the present invention.

[0024] Furthermore, in the following description, descriptions of well-known structures and technologies are omitted to avoid unnecessarily obscuring the concepts disclosed in the present invention.

[0025] In the description of the present invention, it should be noted that, unless otherwise expressly specified and limited, the terms "center", "up", "down", "left", "right", "vertical", "horizontal", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second" and "third" are used for descriptive purposes only and cannot be understood as indicating or implying relative importance. The terms "installed", "connected" and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or an indirect connection through an intermediate medium, or it can be a communication between the internal parts of two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0026] Exemplary embodiments will be described in detail herein, examples of which are illustrated in the accompanying drawings. In the following description, when referring to the drawings, like numbers in different figures represent the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments are not intended to represent all possible embodiments consistent with the present invention. Rather, they are merely examples of methods and systems consistent with certain aspects of the present invention, as detailed in the appended claims.

[0027] The following describes embodiments of the present invention with reference to the accompanying drawings.

[0028] like Figure 1 As shown, the first aspect of the present invention provides an engineering problem solving method based on constitutive model driving, comprising: S1: Mining physical terms of prior knowledge to obtain a set of candidate constitutive terms.

[0029] Wherein, step S1 further includes: S11: Determine the relevant variable parameters according to the target quantity of the engineering problem; S12: Combine the relevant variables into local physical terms; S13: Add exponential functions to multiple local physical terms to perform dimension elimination and obtain a standardized set of candidate constitutive terms.

[0030] Furthermore, in steps S11 to S13, the present invention obtains a set of candidate constitutive terms by mining physical terms of prior knowledge. First, relevant variable parameters are determined according to the target quantity of the engineering problem, that is, the key variables affecting the target quantity are identified by analyzing the physical nature and mathematical description of the specific engineering problem. Subsequently, relevant variables are combined into local physical terms through prior experience or large language model interaction. If there is no prior experience, semantic analysis and knowledge extraction are performed on massive engineering literature based on the large language model through natural language processing technology to identify the physical correlation between variables and generate a combination expression with physical meaning. Finally, exponential functions are added to multiple local physical terms to perform dimensional elimination to obtain a standardized set of candidate constitutive terms. Dimension elimination is to eliminate the dimensional differences between different physical quantities by adding power exponential parameters to each physical term, so that different physical terms can be calculated and compared under the same mathematical framework.

[0031] The candidate constitutive term set in step S1 is selected according to the physical mechanism of the engineering field corresponding to the engineering problem to be solved.

[0032] In one embodiment, the candidate constitutive item set may include any one or more of: input parameter items, boundary constraint items, external influence items, system state items, inherent attribute items, and process parameter items.

[0033] A specific embodiment of the present invention is a welding engineering problem. In the welding engineering problem, the set of candidate constitutive terms includes a current heat input term, a geometric constraint term, a temperature gradient term, a heat accumulation term, a cooling term and a wire diameter term. The current heat input term characterizes the heat input intensity generated by the arc during welding and is calculated by a combination of parameters such as welding current, voltage, and welding speed. The geometric constraint term reflects the constraint effect of the weld geometry on heat conduction and stress distribution. The temperature gradient term describes the spatial distribution characteristics of the temperature field during welding. The heat accumulation term quantifies the heat accumulation effect of the material during welding. The cooling term characterizes the influence of the post-weld cooling process on the material structure and properties. The wire diameter term reflects the influence of the wire geometry parameters on the amount of deposited metal and heat input.

[0034] S2: Perform data enhancement on the experimental data through Gaussian noise function to obtain an expanded training data set.

[0035] Furthermore, in step S2, the present invention performs data enhancement on the experimental data by using a Gaussian noise function to obtain an expanded training data set. Specifically, the present invention generates new training samples by superimposing random noise that conforms to a Gaussian distribution on the original experimental data. First, it is necessary to determine the amplitude range of the noise addition, which is usually set to 5%-15% of the standard deviation of the original data. Then, random perturbations are added to each original data point according to the set noise level to generate multiple variant samples. The Gaussian noise is added in such a way that the variance in the Gaussian process is determined according to the statistical characteristics of the original data and engineering experience. The relationship between data diversity and authenticity is balanced by controlling the noise intensity and the number of generated samples. The expanded training data set contains the original experimental data and all its noise variant samples, forming a larger training set.

[0036] S3: Perform nested optimization on the candidate constitutive term set to obtain the optimal constitutive equation structure and parameter combination.

[0037] Furthermore, in step S3 of the present invention, the optimal constitutive equation structure and parameter combination are obtained by performing nested optimization on the set of candidate constitutive terms. Nested optimization refers to combining the two levels of optimization problems, structure search and parameter optimization, together. The outer layer is responsible for searching for the optimal mathematical expression structure, and the inner layer is responsible for finding the optimal parameter configuration for each candidate structure. The two levels of optimization are nested and co-evolve to ultimately find the global optimal solution.

[0038] Wherein, step S3 further includes: S31: Performing an outer structure search on the candidate constitutive term set by a symbolic regression algorithm to obtain a candidate formula structure set.

[0039] Furthermore, in step S31, the present invention performs an outer structure search on the candidate constitutive term set through a symbolic regression algorithm to obtain a candidate formula structure set. The symbolic regression algorithm is a symbolic expression search method based on a genetic algorithm. The core idea is to represent mathematical expressions as a syntax tree structure and search for the optimal symbol combination in the expression space through the selection, crossover and mutation operations of the genetic algorithm. Specifically, the present invention first initializes a population containing multiple randomly generated mathematical expressions, each expression is composed of candidate constitutive terms combined by different mathematical operators, and then evaluates the performance of each expression through a fitness function, selects an expression with better performance as the parent, and exchanges and combines the subtrees of the two parent expressions through a crossover operation to generate a new child expression. The mutation operation randomly changes certain nodes or subtree structures in the expression, and finally obtains the expression structure set with the best performance after multiple generations of evolution.

[0040] S32: Optimizing inner parameters of multiple formulas in the candidate formula structure set by using a differential optimization algorithm to obtain optimal parameter configurations of the multiple formulas.

[0041] In step S32, the present invention uses a differential optimization algorithm to optimize the inner parameters of multiple formulas in the candidate formula structure set to obtain the optimal parameter configuration of multiple formulas, aiming to search for the optimal parameter combination by simulating the biological evolution process. The algorithm maintains a population containing multiple parameter vectors, and each parameter vector corresponds to a set of candidate parameter values. In each iteration, the algorithm generates a mutation vector for each target vector. The mutation vector is generated by randomly selecting three different individuals from the population and performing linear combination according to a specific mutation strategy. The mutation vector is then cross-operated with the target vector to generate a test vector. Finally, the fitness value of the test vector is compared with the target vector to decide whether to accept the test vector as the next generation individual.

[0042] The differential optimization algorithm in step S32 adopts the best1bin strategy.

[0043] Furthermore, the differential optimization algorithm adopts the best1bin strategy, where best1 means using the best individual in the current population as the basis vector in the mutation operation, and bin means using binomial crossover. The specific mathematical expression is: ; in is the mutation vector, is the individual with the best fitness in the current population. and are two different individuals randomly selected from the population, F is the mutation factor, ranging from 0.4 to 1.0, and the binomial crossover performs a random selection of each dimension of the mutation vector and the target vector according to the crossover probability CR.

[0044] S33: Performing a performance evaluation on the optimal parameter configuration according to a cross entropy loss function and regularization constraints to obtain an optimal constitutive equation structure and parameter combination.

[0045] Step S33 performs a performance evaluation on the optimal parameter configuration according to the cross entropy loss function and the regularization constraint to obtain the optimal constitutive equation structure and parameter combination. The cross entropy loss function is a loss function used to measure the difference between the predicted probability distribution and the true label distribution. The regularization constraint is to add a parameter complexity penalty term to the loss function to prevent overfitting. Step S33 of the present invention performs a performance evaluation process through the above two rules, that is, by calculating the comprehensive loss value of each candidate formula on the verification set to compare the performance of different formulas, and selecting the formula with the smallest loss value as the optimal constitutive equation structure and parameter combination.

[0046] S4: Verify the interpretability of the optimal constitutive equation structure and the parameter combination, and establish a constitutive model for the engineering problem based on the verified optimal constitutive equation structure and parameter combination.

[0047] Furthermore, the comprehensive evaluation of the optimal constitutive equation structure and parameter combination in step S4 of the present invention is intended to compare and verify the mathematical expression obtained by symbolic regression with the actual physical laws to obtain a constitutive model based on the constitutive equation.

[0048] Wherein, step S4 further includes: S41: Physical constraint verification is used to verify the physical rationality of the optimal constitutive equation structure and parameter combination, and obtain the physical constraint verification results.

[0049] Furthermore, the physical constraint verification is achieved through numerical calculation. Specifically, each physical term in the optimal constitutive equation is first subjected to dimensional analysis to ensure that the dimensions on both sides of the equation remain consistent. Taking the material constitutive relationship as an example, during data processing, the stress value from the experimental data is substituted into the left side of the equation, and the corresponding strain, strain rate, and temperature values ​​are substituted into the terms on the right side. The calculated numerical results are then compared with the actual stress values. When the strain increases from 0.001 to 0.01, the calculated stress value must show a monotonically increasing trend. If a negative value or non-physical mutation occurs, the constitutive equation structure does not meet the physical constraint conditions. Another example is the physical rationality test of the temperature effect, which involves analyzing the coefficient of the exponential term. When the temperature increases from room temperature 293K to high temperature 673K, if the coefficient of the exponential term is positive, the stress increases with increasing temperature, which is reasonable in the thermal strengthening phenomenon of the material. If the coefficient of the exponential term is negative, the stress decreases with increasing temperature, which is consistent with the thermal softening law of most metal materials. During the data processing process, the relative error between the predicted stress value and the experimental measurement value at different temperatures is calculated. When the relative error exceeds the set threshold, it is considered that the parameter combination does not meet the physical constraints.

[0050] The final physical constraint verification results are stored in the form of Boolean values, including multiple dimensions of dimensional consistency test results, monotonicity test results, and boundary condition test results. In the results, the constitutive equation is considered to meet the physical rationality requirements only when all physical constraint test items are true.

[0051] S42: Based on the accuracy index and the physical constraint verification results, the optimal constitutive equation structure and parameter combination are evaluated to obtain a constitutive model for the engineering problem.

[0052] Furthermore, the evaluation process in step S42 quantitatively integrates the accuracy metric with the physical constraint verification results. The accuracy metric is calculated by calculating the root mean square error (RMSE) between the predicted and experimental values. The physical constraint verification results are quantified as a score, and the final score is calculated through a weighted fusion approach during the evaluation process. In a specific embodiment, when the comprehensive score exceeds a preset threshold, set to 0.9 in the present invention, the optimal constitutive equation structure and parameter combination have passed comprehensive verification and are formally established as the constitutive model for the engineering problem.

[0053] S5: Solve the engineering problem to be solved by using the engineering problem constitutive model to obtain a solution result.

[0054] The engineering problems to be solved in step S5 include: process parameter optimization problems, cross-scale performance prediction problems, and finite element simulation problems.

[0055] Furthermore, the data processing flow of the process parameter optimization problem includes taking the constitutive model as the core component of the objective function, and calculating the corresponding material performance output by adjusting process parameters such as processing temperature, deformation rate and other input variables; cross-scale performance prediction requires mapping the micro-scale material parameters to the macro-scale engineering performance through the constitutive equation, and scale conversion and parameter transfer are required during data processing; in the finite element simulation problem, the constitutive model is the core of the material property definition, and the continuous stress-strain relationship needs to be discretized into numerical calculations on the finite element nodes.

[0056] like Figure 2 As shown, the present invention also provides an engineering problem solving system driven by a constitutive model, comprising: Mining module 100: used to mine physical terms from prior knowledge to obtain a set of candidate constitutive terms; Enhancement module 200: used to perform data enhancement on the experimental data through a Gaussian noise function to obtain an expanded training data set; Optimization module 300: used to perform nested optimization on the candidate constitutive term set to obtain the optimal constitutive equation structure and parameter combination; Verification module 400: for verifying the interpretability of the optimal constitutive equation structure and the parameter combination, and establishing a constitutive model of the engineering problem based on the verified optimal constitutive equation structure and parameter combination; The solution module 500 is configured as the constitutive model of the engineering problem established by the verification module 400, and is used to solve the engineering problem to be solved and obtain a solution result.

[0057] The present invention also provides an engineering problem solving device driven by a constitutive model, comprising: a memory and at least one processor, wherein instructions are stored in the memory; At least one of the processors calls the instructions in the memory to enable a constitutive model-driven engineering problem solving device to execute any one of the constitutive model-driven engineering problem solving methods described above.

[0058] The present invention also provides a computer-readable storage medium having instructions stored thereon, and when the instructions are executed by a processor, an engineering problem solving method based on constitutive model driving as described above is implemented.

[0059] Furthermore, the engineering problem-solving device driven by a constitutive model provided by the present invention may have relatively large differences due to different configurations or performances, and may include one or more processors (central processing units, CPU), for example, one or more processors and memories, one or more storage media for storing applications or data, such as one or more massive storage devices, wherein the memories and storage media may be short-term storage or persistent storage, and the program stored in the storage medium may include one or more modules, each module may include a series of instruction operations in the engineering problem-solving device driven by a constitutive model, and further, the processor may be configured to communicate with the storage medium to execute a series of instruction operations in the storage medium on the engineering problem-solving device driven by a constitutive model.

[0060] It may also include one or more power supplies, one or more wired or wireless network interfaces, one or more input and output interfaces, and one or more operating systems, such as Windows Server, Mac OS X, Unix, Linux, FreeBSD, etc. Those skilled in the art will appreciate that the structure of the engineering problem-solving device driven by a constitutive model provided in the present invention does not limit the device, and may include more or fewer components than shown in the figure, or combine certain components, or arrange the components differently.

[0061] The following describes a method and system for solving engineering problems driven by a constitutive model according to the present invention in conjunction with a specific embodiment.

[0062] The final model of this embodiment is a K439B high-temperature alloy repair welding hot crack tendency prediction model.

[0063] K439B is a new nickel-based high-temperature alloy casing material resistant to 800°C. It features excellent casting properties and high high-temperature strength. K439B body wire is often used for repair welding. The target quantity is the repair welding hot crack index (CPI). The variables include welding current, single-pass duration, base metal thickness, weld depth, weld area, preheat temperature, interpass temperature, post-weld cooling time to below 500°C, and wire diameter, for a total of nine variables.

[0064] Based on existing experience, the 9 variables were converted into 6 local physical items, and then the existing 32 data were expanded to 32,000 through data enhancement technology as the training set.

[0065] Then the candidate formulas are generated. At the beginning of each iteration, the candidate formulas are generated through the FormulaGenerator class.

[0066] The optimization process is as follows: First generation optimization: Initially generate 100 formulas containing all items from t1 to t6. Examples of candidate formulas: ; ; ; After parameter optimization, the best formula is: , with an accuracy rate of 76%.

[0067] Second generation optimization: Generate new formulas based on the first generation elites, candidate formula examples: ; ; ; After parameter optimization, the best formula is: , with an accuracy rate of 80%.

[0068] Generation 3 to 5: Continue testing different operator combinations and finally optimize to confirm the best formula: , Final accuracy: 89%, Optimal parameters: , that is, a prediction model for hot crack tendency of K439B high-temperature alloy repair welding was obtained.

[0069] The present invention realizes the co-evolution of the structure and parameters of the engineering constitutive model through a double-layer nested optimization strategy. The outer layer uses symbolic regression to search for the optimal formula structure, and the inner layer uses differential evolution to optimize parameter configuration. It breaks through the technical bottleneck of the lack of physical interpretability of traditional machine learning models, effectively solves the problem of data scarcity in the engineering field, and significantly improves the model training effect. At the same time, it ensures that the established constitutive model meets both mathematical accuracy requirements and physical laws, and also achieves balanced optimization of predictive performance and interpretability.

[0070] The established constitutive model of engineering problems can be directly applied to actual engineering scenarios such as process parameter optimization, cross-scale performance prediction, and finite element simulation. It provides an intelligent solution with high precision and strong interpretability for complex engineering problems, greatly improving the efficiency and reliability of engineering design.

[0071] Finally, it should be noted that the above embodiments are merely illustrative of the technical solutions of the embodiments of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they may still modify the technical solutions described in the aforementioned embodiments, or replace some of the technical features therein with equivalents; and such modifications or replacements do not deviate from the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention. Any changes or replacements that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be covered by the scope of protection of the present invention.

Claims

1. A method for solving engineering problems based on constitutive model driving, characterized in that: include: S1: Mining physical terms from prior knowledge to obtain a set of candidate constitutive terms; S2: Perform data enhancement on the experimental data through Gaussian noise function to obtain an expanded training data set; S3: performing nested optimization on the candidate constitutive term set to obtain the optimal constitutive equation structure and parameter combination; S4: verifying the interpretability of the optimal constitutive equation structure and the parameter combination, and establishing a constitutive model of the engineering problem based on the verified optimal constitutive equation structure and parameter combination; S5: Solve the engineering problem to be solved by using the engineering problem constitutive model to obtain a solution result.

2. The method for solving engineering problems based on constitutive model driving according to claim 1, characterized in that: Step S1 further comprises: S11: Determine relevant variable parameters based on the target quantity of the engineering problem; S12: Combine related variables into local physical terms; S13: Add exponential functions to multiple local physical terms to perform dimension elimination and obtain a standardized set of candidate constitutive terms.

3. The method for solving engineering problems based on constitutive model driving according to claim 1, characterized in that: The candidate constitutive term set in step S1 is selected according to the physical mechanism of the engineering field corresponding to the engineering problem to be solved.

4. The method for solving engineering problems based on constitutive model driving according to claim 1, characterized in that: Step S3 further comprises: S31: performing an outer structure search on the candidate constitutive term set by a symbolic regression algorithm to obtain a candidate formula structure set; S32: Optimizing inner parameters of multiple formulas in the candidate formula structure set using a differential optimization algorithm to obtain optimal parameter configurations for the multiple formulas; S33: Performing a performance evaluation on the optimal parameter configuration according to a cross entropy loss function and regularization constraints to obtain an optimal constitutive equation structure and parameter combination.

5. The method for solving engineering problems based on constitutive model driving according to claim 4, characterized in that: The differential optimization algorithm in step S32 adopts the best1bin strategy.

6. The method for solving engineering problems based on constitutive model driving according to claim 1, characterized in that: Step S4 further comprises: S41: Physical constraint verification is used to verify the physical rationality of the optimal constitutive equation structure and parameter combination, and obtain the physical constraint verification results; S42: Based on the accuracy index and the physical constraint verification results, the optimal constitutive equation structure and parameter combination are evaluated to obtain a constitutive model for the engineering problem.

7. The method for solving engineering problems based on constitutive model driving according to claim 1, characterized in that: The engineering problem to be solved in step S5 includes: Process parameter optimization problems, cross-scale performance prediction problems, and finite element simulation problems.

8. An engineering problem solving system driven by a constitutive model, characterized in that: include: Mining module: used to mine physical terms from prior knowledge and obtain a set of candidate constitutive terms; Enhancement module: used to enhance the experimental data through Gaussian noise function to obtain an expanded training data set; Optimization module: used to perform nested optimization on the candidate constitutive term set to obtain the optimal constitutive equation structure and parameter combination; Verification module: used to verify the interpretability of the optimal constitutive equation structure and the parameter combination, and establish a constitutive model of the engineering problem based on the verified optimal constitutive equation structure and parameter combination; A solution module is configured as the constitutive model of the engineering problem established by the verification module, and is used to solve the engineering problem to be solved and obtain a solution result.

9. An engineering problem solving device driven by a constitutive model, characterized in that: include: a memory and at least one processor, wherein instructions are stored in the memory; At least one of the processors calls the instructions in the memory to enable a device for solving engineering problems driven by a constitutive model to execute a method for solving engineering problems driven by a constitutive model as claimed in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores instructions, and when the instructions are executed by the processor, the method for solving engineering problems based on constitutive model driving according to any one of claims 1 to 7 is implemented.

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